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NATIONAL BANK OF POLAND W O R K I N G PA P E R No. 104

Multistate asymmetric ACD model: an application to order dynamics in the EUR/PLN spot market

Katarzyna Bie-Barkowska

Warsaw 2011

Katarzyna Bie-Barkowska ­ National Bank of Poland, Financial System Depar tment, ul. witokrzyska 11/21, 00-919 Warsaw, Poland, phone: +48 783 306 586, email: [email protected]; Institute of Econometrics, Warsaw School of Economics, Al. Niepodlegloci 164, 02-554, Warsaw, Poland, email: [email protected]

The author wants to thank the Thomson Reuters for providing the data from the Reuters Dealing 3000 Spot Matching system. Helpful remarks of Roxana Halbleib, Fabian Kr¨ger, Lidan u Li, Mateusz Pipie´, Winfried Pohlmeier, Pawe Sobolewski and the participants of the faculty n l seminars at the Warsaw School of Economics and at the University Konstanz are fully appreciated. Any remaining errors are the responsibility of the author. The views and opinions presented herein are those of the author and do not have to necessarily reflect those of the National Bank of Poland. ´ National Bank of Poland, Financial System Department, ul. Swietokrzyska 11/21, 00-919 Warsaw, Poland, phone: +48 783 306 586, email: [email protected] Institute of Econometrics, Warsaw School of Economics, Al. Niepodleglo´ci 164, 02-554, Wars saw, Poland, email: [email protected]

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Abstract

Abstract This paper examines a process of order submissions and cancellations in the interbank order driven market of the EUR/PLN currency pair. Our contribution to the existing literature is twofold. We generalize the Asymmetric ACD model (AACD) of Bauwens & Giot (2003) with respect to more than two competing risks. It results in the flexible multistate econometric model for durations between moments in which order submissions or cancellations take place. Thanks to the Multistate AACD model we are able to examine timing of order submissions/cancellations that (1) take place on different sides of the market and (2) vary according to the level of order aggressiveness. We show how to simulate from the proposed Multistate Asymmetric ACD model, which enables us to study the transition probabilities between selected events. We investigate different market microstructure factors that exert an influence on the intraday pattern of order submission or cancellation strategies.

JEL classification: G10, F 30, C30 Keywords: asymmetric ACD model, order dynamics, intraday liquidity

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Introduction

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Introduction

Order dynamics is an important foundation for the quality of an order-driven market. The various factors that determine whether or not to place an order of a particular type at a particular moment influence the process whereby liquidity is supplied to the market via limit orders or is demanded from the market via market orders. Through detailed insight into the behavior of market participants it is also possible to understand the process of price formation. The disclosure of factors that determine the fluctuation of liquidity is of primary importance for both market clients and for regulators as an undesirable liquidity squeeze can lead to extreme and undesirable price movements as seen during the most recent financial turmoil of 2008-2009. The paper analyzes the process of order submissions and cancellations in the interbank order driven market of the EUR/PLN currency pair. In order to capture the entirety of the dynamics of the order book, we present a generalized version of the Asymmetric ACD model that we will call the Multistate Asymmetric ACD model (MAACD). Within this wider setup we are able to describe the expected durations between moments when orders, classified according to selected "classes of aggressiveness", will arrive to the market or will be withdrawn from it. Thus, we are able to differentiate between potential factors governing the pace at which liquidity is exhausted or is replenished. Our work has been inspired by the empirical study of Lo & Sapp (2008) where the intraday mixture of best limit orders and market orders was analyzed by means of the standard asymmetric ACD model of Bauwens & Giot (2003). The study tests the impact of different factors not only on whether a trader chooses a particular order type but also on the timing of such a decision. The inclusion of time in the modeling framework allows the user to investigate time-varying preferences with regard to the arrival of particular orders in a continuously changing market environment. The precedence of market orders over limit orders (or vice versa) and the order clustering effects have been investigated from the perspective of time-varying liquidity and information-related market characteristics. In this paper our goal is to further develop the work of Lo & Sapp (2008) in an effort to contribute to the empirical literature on order dynamics in two main dimensions. First, as opposed to Lo & Sapp (2008), we do not focus only on the best orders submitted within the system (i.e. market orders or best limit orders). Instead, we take into account all of the orders that enter into the trading system and we classify them according to their level of aggressiveness (i.e. the likelihood of being executed). Second, we model both sides of the order book jointly and simultaneously differentiate between the bid and ask sides of the market. Such a modelling strategy allows us to account for the possible endogeneity among different moments where 1 buy and/or sell orders are posted or cancelled. Additionally, we demonstrate how to easily simulate from the MAACD model. Such a simulation algorithm can be helpful if we want to test the properties of the model. For example, we can easily simulate a most probable sequence according to which orders ienter theBmarket oor areo with- d N a t o n a l a n k f P l a n drawn from it. The obtained transition probability estimates can be compared with the existing theoretical (see Parlour (1998); Foucault (1999) and Goettler, Parlour

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Introduction

differentiate between the bid and ask sides of the market. Such a modelling strategy allows us to account for the possible endogeneity among different moments where buy and/or sell orders are posted or cancelled. Additionally, we demonstrate how to easily simulate from the MAACD model. Such a simulation algorithm can be helpful if we want to test the properties of the model. For example, we can easily simulate a most probable sequence according to which orders enter the market or are withdrawn from it. The obtained transition probability estimates can be compared with the existing theoretical (see Parlour (1998); Foucault (1999) and Goettler, Parlour & Rajan (2005)) or empirical (see Biais (1995); Hall & Hautsch (2006) and Hall & Hautsch (2007)) results from the literature concerning order book dynamics. With the application of the MAACD model we are also able to investigate how the arrival time of orders will relate to each other when they are (1) characterized by differing levels of aggressiveness and are (2) posted on different market sides. We also enrich our model with a variety of explanatory variables reflecting a continually changing market environment as well as the state of the order book. We then verify their impact on trader decisions with respect to the type of order placed and the time of such a submission or cancellation. This modelling framework allows us to verify selected theoretical microstructure hypotheses in a more explicit manner. Our model is very much related to the studies of Hall & Hautsch (2006) and Hall & Hautsch (2007) where the multidimensional autoregressive conditional intensity (ACI) function has been developed in order to account for the instantaneous arrival rates of different order types. In a close analogy to the multidimensional ACI model, the MAACD model can also account for the complex dynamics of the order book. Both models can describe the arrival rates characterizing particular classes of orders as well as the interdependence between these individual processes. Therefore, our effort is to apply another flexible econometric specification that can adequately describe a complicated intertemporal game of order submissions while at the same time being tractable and easy to estimate and/or to simulate. The second aim of our analysis is to enrich what is currently a very scarce area of literature concerning the microstructure of currency markets in emerging economies. From the econometric viewpoint, the process of order submissions and cancellations in our modeling approach is reflected as an ordered point process. Accordingly, we model the temporal accelerations and/or decelerations in the pace of dealer activity with the highest resolution possible. In fact, the driving forces for order flow in our study are much different than those for stocks or major currency markets. Clearly, zloty and euro are not treated as substitutes with regards to level of risk undertaken; thus, the willingness to invest in emerging market currencies is closely linked to the changes in global risk aversion versus the risk appetite as well as to the fundamental 2 foundings of the Polish economy as compared to the other CE3 members (i.e. Hungary and the Czech Republic). The paper is structured as follows. In section 2 we introduce the theoretical argumentation for our model. We present a survey of the theoretical and empirical literature that deals with different aspects of order submission regularities. We also touch on the fact that there are market microstructure hypotheses that refer to selected factors which impact order choice. In the section 3 we present the Reuters WORKING PAPER No. 104 Dealing 3000 Spot Matching System and we introduce the data to be used in the empirical study. Section 4 contains the theoretical econometric background for the

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thus, the willingness to invest in emerging market currencies is closely linked to the changes in global risk aversion versus the risk appetite as well as to the fundamental Introduction foundings of the Polish economy as compared to the other CE3 members (i.e. Hungary and the Czech Republic). The paper is structured as follows. In section 2 we introduce the theoretical argumentation for our model. We present a survey of the theoretical and empirical literature that deals with different aspects of order submission regularities. We also touch on the fact that there are market microstructure hypotheses that refer to selected factors which impact order choice. In the section 3 we present the Reuters Dealing 3000 Spot Matching System and we introduce the data to be used in the empirical study. Section 4 contains the theoretical econometric background for the specifications of the Multistate Asymmetric ACD model. In the sections 5 and 6 we present the results of the empirical analysis. The conclusion sums up the results of the study and comments their importance.

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Literature Overview and Economic Hypotheses

There is a large strand of literature that underlines the informative content of time as one of the latent factors that influences the behavior of market participants. The theoretical microstructure models that implicitly entwine the concept of time date back to studies of Admati & Pfleiderer (1988), Diamond & Verrecchia (1987) and Easley & O'Hara (1992). In the first model, fluctuations in trading activity signal the arrival of new information. When trading intensity is high it is easier for informed traders to hide their strategic intensions. Simultaneously, liquidity traders (uninformed traders) who are discretionary (i.e. they can choose the periods in which they trade) also prefer to trade in such heavy periods as their activity does not induce undesirable price movements. On the other hand, periods of slow trading where there are no discretionary liquidity traders in the market is an area where there will be a relatively large fraction of informed traders present. This hypothesis is often described in the literature as "slow trading means informed trading". Informational content of trade activity is also underlined in the model of Easley & O'Hara (1992). In their approach, periods of increased trading signal the presence of informed traders; thus, their model is often described as "no trade means no news". In the model of Diamond & Verrecchia (1987), due to the presence of the short selling restrictions in some capital markets, informed traders cannot speculate on bad information. Therefore, if the bad news arrives trading activity declines. The 3

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Dealing 3000 Spot Matching System and we introduce the data to be used in the empirical study. Hypotheses Literature Overview and EconomicSection 4 contains the theoretical econometric background for the specifications of the Multistate Asymmetric ACD model. In the sections 5 and 6 we present the results of the empirical analysis. The conclusion sums up the results of the study and comments their importance.

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Literature Overview and Economic Hypotheses

There is a large strand of literature that underlines the informative content of time essence of this phenomenon is often described behavior of market bad information". as one of the latent factors that influences theas "no trading meansparticipants. The theoretical microstructure models that implicitly entwine the concept of time date The aforementioned models underline the importance of time in explaining various back to studies of Admati & Pfleiderer (1988), Diamond & Verrecchia (1987) and strategic information-motivated intentions of market participants. The theoretical Easley & O'Hara (1992). In the first model, fluctuations in trading activity signal framework refers to a price-driven market with a single market maker. On the other the arrival of new information. When trading intensity is high it is easier for inhand, much theoretical research has also been carried out in order to fully underformed traders to hide their strategic intensions. Simultaneously, liquidity traders stand the order submission strategies in an automated order-driven market (limit (uninformed traders) who are discretionary (i.e. they can choose the periods in order market). Such trading mechanisms have gained in importance over the last which they trade) also prefer to trade in such heavy periods as their activity does decade and today limit order markets dominate trading in stocks and foreign exnot induce undesirable price movements. On the other hand, periods of slow trading change markets1 . In the automated order-driven markets, dealers willing to trade where there are no discretionary liquidity traders in the market is an area where can enter either a market order which is immediately executed at the prevailing there will be a relatively large fraction of informed traders present. This hypothbid or ask quotes or they can post a limit order that waits for a given time period esis is often described in the literature as "slow trading means informed trading". for execution at a more favorable price. Market orders were initially perceived as Informational content of trade activity is also underlined in the model of Easley & information-motivated. Since superior information can quickly lose its value, the O'Hara (1992). In their approach, periods of increased trading signal the presence of use of market orders always guarantees an immediate execution. Limit orders are informed traders; thus, their model is often described as "no trade means no news". perceived as patient, passive and liquidity-motivated (e.g. Glosten (1994) and Seppi In the model of Diamond & Verrecchia (1987), due to the presence of the short (1997)). Most recently the conviction about sole informational content of market selling restrictions in some capital markets, informed traders cannot speculate on orders has been challenged and there is a widespread notion that limit orders and bad information. Therefore, if the bad news arrives trading activity declines. The the whole process of the liquidity provision can be also initiated by informed traders essence of this phenomenon is often described as "no trading means bad information". (e.g. Bloomfeld, O'Hara & Saar (2005); Anand, Chakravarty & Martell (2005) and 3 Hasbrouck & Saar (2009)). The decision to post a limit time in explaining various The aforementioned models underline the importance of order is always associated with a trade-off between the potential gain from obtaining a better price and the strategic information-motivated intentions of market participants. The theoretical potential risk of to a price-driven market beinga"picked-off". With a limit order a framework refers either non-execution or with single market maker. On the other trader muchget a better research has alsothere is also the riskorder to fully underhand, can theoretical price; however, been carried out in that the order may never be executed. On the other hand, as the price of limit orders are fixed, (limit stand the order submission strategies in an automated order-driven market there is an additional Such that the mechanisms become mispriced when newover the last order market). risk trading orders may have gained in importance information arrives. and today limit order markets dominate trading in stocks and executedexdecade This adverse selection risk may lead to losses if a limit order is foreign at an unfavorable price. the automated order-driven markets, dealers willing to trade change markets1 . In The dilemma is determining what kind of order to choose and when to submit given order. All of this provides the basis for numerous prevailing can enter eithera a market order which is immediately executed at the theoretical and empirical research studies on the dynamics that waits for book. bid or ask quotes or they can post a limit orderof a limit order a given time period for execution at a more favorable price. Market orders were initially perceived as Theoretical dynamic equilibrium models that describe the order choice problem as information-motivated. Since superior information can quickly lose its value, the a sort of a multi-agent bargaining game have been formulated by Parlour (1998), use of market orders always guarantees an immediate execution. Limit orders are Foucault (1999), Foucault, Kadan & Kandel (2005), Goettler et al. (2005) and Rosu perceived as patient, passive and liquidity-motivated (e.g. Glosten (1994) and Seppi (2009). In the first two studies some testable hypotheses with regard to the process (1997)). Most recently the conviction about sole informational content of market of order submissions have been formulated. In Parlour (1998), the individual order orders has been challenged and there is a widespread notion that limit orders and 1 Examples ofprocess of books are: the Euronext Paris, the SEAQinitiated by informedmarkets), the whole limit order the liquidity provision can be also or the NASDAQ (stock traders the Reuters DealingO'Hara & Saar (2005); Anand, and the MTS (bonds). (e.g. Bloomfeld, 3000 and the EBS (currency pairs) Chakravarty & Martell (2005) and Hasbrouck & Saar (2009)). The decision to post a limit order is always associated 4 with a trade-off between the potential gain from obtaining a better price and the WORKING PAPER No. 104 potential risk of either non-execution or being "picked-off". With a limit order a trader can get a better price; however, there is also the risk that the order may never be executed. On the other hand, as the price of limit orders are fixed, there

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bid or ask quotes or they can post a limit order that waits for a given time period Literature Overview perceived as for execution at a more favorable price. Market orders were initiallyand Economic Hypotheses information-motivated. Since superior information can quickly lose its value, the use of market orders always guarantees an immediate execution. Limit orders are perceived as patient, passive and liquidity-motivated (e.g. Glosten (1994) and Seppi (1997)). Most recently the conviction about sole informational content of market orders has been challenged and there is a widespread notion that limit orders and the whole process of the liquidity provision can be also initiated by informed traders (e.g. Bloomfeld, O'Hara & Saar (2005); Anand, Chakravarty & Martell (2005) and Hasbrouck & Saar (2009)). The decision to post a limit order is always associated with a trade-off between the potential gain from obtaining a better price and the potential risk of either non-execution or being "picked-off". With a limit order a trader can get a better price; however, there is also the risk that the order may never be executed. On the other hand, as the price of limit orders are fixed, there is an additional risk that the orders may become mispriced when new information arrives. This adverse selection risk may lead to losses if a limit order is executed at an unfavorable price. The dilemma is determining what kind of order to choose and when to submit a given order. All of this provides the basis for numerous theoretical and empirical research studies on the dynamics of a limit order book. Theoretical dynamic equilibrium models that describe the order choice problem as a sort of a multi-agent bargaining game have been formulated by Parlour (1998), Foucault (1999), Foucault, Kadan & Kandel (2005), Goettler et al. (2005) and Rosu (2009). In the first two studies some testable hypotheses with regard to the process of order submissions have been formulated. In Parlour (1998), the individual order choices depend on the state of the Euronext Paris, the the awaitedNASDAQ (stock markets), 1 Examples of limit order books are: the order book and SEAQ or the arrival rate of market orders over Dealing 3000 and of the day. Traders in and the MTS (bonds). the aftereffects the Reuters the remainder the EBS (currency pairs) this case anticipate of their actions on other market participants. Even if there is no information-based 4 incentive to trade in this model, some regularities in the patterns of order submission can be obtained. Parlour (1998) predicts that after a market buy (sell), the most probable order would be limit sell (buy). It is because the payoff of a limit sell (buy) order (the utility gain) depends on the probability of execution. If the probability rises after a market buy (sell), the order book will be reduced by at least one unit on the ask (bid) side. The limit sell (buy) will gain the priority of execution and thus it will be more profitable. Such a phenomenon has been named "a crowding out effect" because orders of a given type that are submitted on one side of the order book "crowd out" other orders by making them unattractive. Accordingly, market orders submitted on the ask (bid) side of the market are crosscorrelated with limit orders on the bid (ask) side of the market. This regularity is summed up by the following hypothesis: · H1: The probability of observing a limit sell (limit buy) order is larger if the previous transaction was a market buy (market sell), than if it was a market sell (market buy). Another hypothesis has been formulated with regard to market orders. Once a market buy (sell) order is observed, a limit sell (buy) order allows for a higher utility gain than a market sell (buy). Traders who want to sell would rather choose limit sells than market sells. Thus, the liquidity provision is more profitable on the ask side of the market. This is another type of a the "crowding out effect" which predicts N a t o n a l B a n f o l a n serial correlation in the order flow. This clustering ofi market ordersk ono onePmarket d side can arise either from pure liquidity dynamics or from informed trading. Thus, a second hypothesis:

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Literature Overview and Economic Hypotheses

· H1: The probability of observing a limit sell (limit buy) order is larger if the previous transaction was a market buy (market sell), than if it was a market sell (market buy).

Another hypothesis has been formulated with regard to market orders. Once a market buy (sell) order is observed, a limit sell (buy) order allows for a higher utility gain than a market sell (buy). Traders who want to sell would rather choose limit sells than market sells. Thus, the liquidity provision is more profitable on the ask side of the market. This is another type of a the "crowding out effect" which predicts serial correlation in the order flow. This clustering of market orders on one market side can arise either from pure liquidity dynamics or from informed trading. Thus, a second hypothesis: · H2: The probability of a market sell (market buy) is larger if the previous transaction was a market sell (market buy) than if it was a market buy (market sell). The aforementioned hypotheses are based on the assumption that traders optimize their order choice with regard to (1) the state of the order book (which is determined by the past behavior of traders), and (2) the anticipated actions of other rational traders. The "crowding out mechanism" can also be used to formulate hypotheses that relate directly to the depth of the order book (see also in Hall & Hautsch (2006) and Hall & Hautsch (2007). Thus, a third hypothesis: 5 · H3: Increase in the depth on the ask (bid) side increases the aggressiveness of market trading on the ask (bid) side. The rationale behind this hypothesis is this: a limit order placed in a book has a lower probability of execution when there are already many orders standing in front of it. Accordingly, the contemporaneous mixture of orders will be shifted toward market orders. Some regularity with regard to the order sequencing has been discovered from the stochastic sequential model of Goettler et al. (2005). In this very general modeling setup, traders can submit multiple limit orders at different prices and trade different quantities. The generalization of this model comes with a cost and the equilibrium must be solved numerically. The simulation results depict a "diagonal effect", which means that market buys are more probable after market buys then after market sells. This agrees with the second hypothesis (H2). Moreover, market orders are often followed by limit orders on the same side of a market. The logic is that after an increase (decrease) of the consensus value of an asset, sell (buy) orders become mispriced. This induces a flow of buy (sell) market orders that "pick off" these limit orders. In the dynamic equilibrium model of Foucault (1999), the proportion of limit to market orders depends on the volatility of an asset. An increase in the fundamental risk of an investment magnifies the risk of being picked-off. Thus, the reservation prices of limit orders become less aggressive and the bid-ask spread widens. As a consequence of this, the use of market orders becomes more expensive and traders opt for limit orders. The mixture of orders shifts in favor of limit orders but the trading activity declines. In this case the following hypotheses arise:

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· H4: An increase in the bid-ask spread decreases the probability of a market order and increases the probability of an aggressive limit order.

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Literature Overview and Economic Hypotheses

In the dynamic equilibrium model of Foucault (1999), the proportion of limit to market orders depends on the volatility of an asset. An increase in the fundamental risk of an investment magnifies the risk of being picked-off. Thus, the reservation prices of limit orders become less aggressive and the bid-ask spread widens. As a consequence of this, the use of market orders becomes more expensive and traders opt for limit orders. The mixture of orders shifts in favor of limit orders but the trading activity declines. In this case the following hypotheses arise:

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· H4: An increase in the bid-ask spread decreases the probability of a market order and increases the probability of an aggressive limit order. · H5: An increase in the volatility decreases the probability of a market order and increases the probability of an aggressive limit order. In the dynamic equilibrium model of Foucault et al. (2005) the concept of time has been introduced through the cost of waiting. The proportion of market and limit orders depends on a trade-off between the cost of immediacy (the bid-ask spread) and the cost of delayed execution (the waiting costs). Within this framework, waiting costs are proportional to the time required for traders to complete their transactions. Therefore, the increase in waiting cost prompts liquidity suppliers to bid or to ask more aggressively. This logic supports the fifth hypothesis (H5). According to the 6 model, the amount by which traders improve upon the prevailing quotes depends on the size of the bid-ask spread. In order-driven markets, the risk embedded in limit orders can be limited by an appropriate monitoring market information. Once the submitted orders become mispriced traders can always cancel or revise them in order to mitigate the freeoption risk or the risk of no-execution. The literature provides many examples of information-motivated cancellations of limit orders. Hasbrouck & Saar (2009) document that over one-third of nonmarketable limit orders for NASDAQ-listed stocks on the INET are cancelled within two seconds. They show that the use of such "fleeting orders" is a very recent phenomenon that stems from improved technology and the active trading culture. Fong & Liu (2010) show that order revisions generate a net economic benefit for market participants and that the process of order cancellations/revisions is based on the continual monitoring of market conditions. Liu (2009) proposes a formal model where the relationship between order submission risks and cancellation/revision activity has been investigated. He predicts that if the bid-ask spread widens then the cancellation rates will fall. If the bid-ask spread is large the expected cost of execution of an limit order at an undesirable price as well as the expected cost of non-execution is low. The same relationship is predicted by Hasbrouck & Saar (2009). According to their "cost-of-immediacy" hypothesis, if the cost of immediate execution (i.e. the bid-ask spread) decreases, the "gravitational pull" of immediate execution with a market order rises. The limit orders that were placed inside the quotes and were not purely liquidity-motivated are then are changed to market orders. Thus, we have a sixth hypothesis: · H6: A decrease in the bid-ask spread increases the probability of a limit order cancellation.

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In agreement with the model described by Foucault (1999), cancellation activity N a t i o n a l B a n k o f P o l a n d should be also higher if volatility rises. Large and unpredictable swings of the exchange rate increase the risk that the order will be mispriced (the free option risk of a limit order); thus, we predict that the following hypothesis should be true:

price as well as the expected cost of non-execution is low. The same relationship is predicted by Hasbrouck & Saar (2009). According to their "cost-of-immediacy" Literature Overview and Economic Hypotheses hypothesis, if the cost of immediate execution (i.e. the bid-ask spread) decreases, the "gravitational pull" of immediate execution with a market order rises. The limit orders that were placed inside the quotes and were not purely liquidity-motivated are then are changed to market orders. Thus, we have a sixth hypothesis: · H6: A decrease in the bid-ask spread increases the probability of a limit order cancellation. In agreement with the model described by Foucault (1999), cancellation activity should be also higher if volatility rises. Large and unpredictable swings of the exchange rate increase the risk that the order will be mispriced (the free option risk of a limit order); thus, we predict that the following hypothesis should be true: · H7: An increase in the volatility (2003); Ranaldo (2004); of a limit order in limit order markets (Bae, Jang & Parkincreases the probabilityVerhoeven, Ching & Ngcancellation. (2003); Pascual & Veredas (2004); Ellul, Holden, Jain & Jennings (2007); Lo & Sapp (2008); of high-resolution quote datasets has Biais (1995) is one in empirThe availability and others). The empirical analysis of spurred an interestof the first studies on this of the The study investigates There is a large body of empirical ical verification matter.hypotheses stated above.order sequences on the Paris Bourse and finds some systematic patterns. of different market conditions on order choice literature that deals with the impact For example, it empirically demonstrates "the diagonal effect", which is the clustering of orders of the (2004); Verhoeven, (1995) in limit order markets (Bae, Jang & Park (2003); Ranaldo same type. Biais Ching proposes following explanations for this. 7 First,Holden, Jain & Jennings orders into & Ng (2003); Pascual & Veredas (2004); Ellul, traders may split large (2007); Lo small ones in an effort to limit a empirical analysis of Biais (1995) is one of the first & Sapp (2008); and others). The price reaction. Second, traders may imitate other traders'on this matter. The study investigates order sequences on the selected marstudies behavior ("piggyback"). Third, traders may indeed react to Paris Bourse ket eventssome systematic patterns. For example, itof Biais (1995) spurred serious and finds in a similar way. Although the findings empirically demonstrates "the interest in confirming suchthe clustering of orders of the same type. Biais (1995) diagonal effect", which is regularities within different markets, the majority of the econometric tools that have beenfor this. were strictly static in nature. The studies proposes following explanations applied First, traders may split large orders into of Verhoeven et al. (2003); Ranaldo (2004) and Ellul et al. (2007) useimitate other small ones in an effort to limit a price reaction. Second, traders may logit regressions. Such specifications can adequately account forindeed react to selected martraders' behavior ("piggyback"). Third, traders may numerous exogenous factors thatevents an a similar way. order choice; however, of Biais (1995) spurredaccount ket have in impact on the Although the findings they cannot take into serious the role of time variation regularities within different Trading the majority occur interest in confirming suchbetween order submissions. markets, needs do not of the synchronically among traders and applied were evoked by the in nature. The studies econometric tools that have been they may be strictly static actions taken by other market participants2 . Static models (2004) and Ellul for al. (2007) use logitsuch as of Verhoeven et al. (2003); Ranaldo do not account et the casual effects regrespossible spill-overs between the arrival rates of various order types exist. Moreover, sions. Such specifications can adequately account for numerous exogenous factors nearly all an impact on the order that have been they cannot take into account that have of the empirical findings choice; however, reported depict stock markets; there are only a variation between order currency trading (Bloomfeld et not occur the role of time few exceptions devoted to submissions. Trading needs do al. (2005), Lo & Sapp (2008)). synchronically among traders and they may be evoked by the actions taken by other market participants2 . Static models do not account for the casual effects such as possible spill-overs between the arrival 3 Market and Data rates of various order types exist. Moreover, nearly all of the empirical findings that have been reported depict stock markets; there are only a few exceptions devoted to currency among all the currency (2005), The FX market of the Polish Zloty is the most liquidtrading (Bloomfeld et al.markets Lo & Central European emerging economies3 . Spot transactions can be executed of theSapp (2008)). on the OTC market using the Reuters Dealing Direct system, via a voice broker or by telephone. About half of all trades is conducted via the Reuters Dealing 3000 3 Market and Data Spot Matching System (RDSMS) and the importance of this platform is continually The is most pronounced in the automated FX markets liquid among all the informationmarkets FX market of the Polish Zloty is the most where, based upon the currency obtained This of the Central European of trades areeconomies3 . Spotintransactions can The executed from FX dealers, about 80% emerging purely speculative their motivation. be remainder are motivated market using the on the OTC by real trading needs.Reuters Dealing Direct system, via a voice broker or 3 According to the by telephone. survey of halfmarket activity conducted by thevia the Reuters Dealing 3000 About FX of all trades is conducted Bank for International Settlements BIS (2007), the average daily turnover in interbank spot transactions amounted to 4,851 million Spot Matching System (RDSMS) and the importance of this platform is continually

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USD in April 2007. This market is, therefore, nearly two times bigger than the spot market for the where the average daily turnover amounted to 2,959 million USD in April 2007 This is most pronounced in the automated FX markets where, based upon the information obtained and about three times more liquid than the market for the Czech Koruna (1,630 million USD). from FX dealers, about 80% of trades are purely speculative in their motivation. The remainder are motivated by real trading needs.

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market participants2 . Static models do not account for the casual effects such as possible spill-overs between the arrival rates of various order types exist. Moreover, Market and Data nearly all of the empirical findings that have been reported depict stock markets; there are only a few exceptions devoted to currency trading (Bloomfeld et al. (2005), Lo & Sapp (2008)).

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Market and Data

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The FX market of the Polish Zloty is the most liquid among all the currency markets of limit order markets (Bae, Jang & economies3 . Spot transactions can be executed in the Central European emerging Park (2003); Ranaldo (2004); Verhoeven, Ching on Ng (2003);market using the Reuters Dealing Holden, Jain &via a voice(2007); Lo & the OTC Pascual & Veredas (2004); Ellul, Direct system, Jennings broker or bySapp (2008);About half ofThe trades is conducted via the Reutersone of the3000 telephone. and others). all Dealing first & limit order markets (Bae, Jang empirical analysis of Biais (1995)Verhoeven, Ching in & Park (2003); Ranaldo (2004); is Spot Matching matter. (RDSMS) and the importancesequences on the is continually this studies on this System&The study investigates order of Jain platform Paris Bourse & Ng (2003); Pascual Veredas (2004); Ellul, Holden, & Jennings (2007); Lo growing over the subsequent years. It For example, itand transparent electronic "the and finds some and others). The empirical analysis ofempirically demonstrates brosystematic patterns. is a very liquid Biais (1995) is one of the first 2 & Sapp (2008); This is most pronounced in the automated FX markets where, based upon the information obtained kerage system, operating as an order-drivenorders ofthat can automatically (1995) market match diagonaldealers, matter. Thetrades are purely speculative inthe same on the Paris Bourse from FX on this about 80% ofthe clustering of their motivation. Biais studies effect", which is study investigates order sequences type. The remainder incoming following sell orders once their prices agree. FX dealers can submit either proposes buy real explanations are motivated byand trading needs. for this. example, it empirically demonstrates "the and finds some systematic patterns. For First, traders may split large orders into 3 Accordingmarket orders;FX marketorders are perceived as liquidity-consuming and aglimit or to in an effort to limit aactivity reaction. by the Bank for International Settlements small ones the survey of marketclustering of orders of thetraderstype. imitate(1995) price conducted Second, same may Biais other diagonal effect", which is the BIS (2007), the average daily turnover in executed spot transactions amounted to limit orders interbank against gressive since they("piggyback"). Third, traders may most competitive 4,851 million traders' behavior are immediately this. First, traders may react large ordersmarindeed split to selected into proposes following explanations for nearly two times bigger than the spot market for the USD in April 2007. This market is, therefore, in the order book. As far as Although the findings of system is concerned, traders the transparency of the Biais (1995) spurred serious ket events in a similar to limit a price reaction. Second, traders may imitate other Hungarian Forint where the average daily turnover amounted to 2,959 million USD in April 2007 small ones in an effort way. can about three times more liquid than the market and bid prices that the majority to the best interest in confirming such regularities within different markets, correspond of and observe continually changingThird,ask for the Czech Koruna (1,630 million USD). traders' behavior ("piggyback"). traders may indeed react to selected marmost competitive buy and sell limit orders stored in the order book. They can also econometric tools that have been applied were strictly static (1995) spurred studies ket events in a similar way. Although the findings of Biais in nature. The serious 8 limit orders al. (2007) seeVerhoeven et al.of best ask and best bid and Ellul et (the depth use the best ask of the whole size (2003); regularities within different markets, the at logit regresinterest in confirming such Ranaldo (2004) majority of the and the depth at the best can adequately if this size does not exceed 10 M.factors sions. Such specifications bid) but only were strictly static in nature. The studies account for numerous exogenous EUR. econometric tools that have been applied If it is the an impactquantity order choice; however, hidden and the sign "R" (reguthe on the of the is they cannot take that have case, al. (2003); Ranaldo whole depthEllul et al. (2007) use into account of Verhoeven et (2004) and logit regreslar order) appears next to between orderor the best bidTrading needs do a solution the best ask quotation. Such not occur the role of time variation can adequatelysubmissions. numerous exogenous factors sions. Such specifications account for allows for the size of large orders they may be evoked by the actions taken by to be synchronicallyimpact on the ordersubmitted to the system at thetake into account among traders and choice; however, they cannot best prices other that have an hidden. participants2 . Static models do not account for the all other (less competprice nor the quantity of casual effects such as market Traders can see neither the order submissions. Trading needs do not occur the role of time variation between itive) orders placed between the arrival rates of various order types pair, traders also possible spill-overs in the system. Unlike the EUR/USD currency exist. Moreover, synchronically among traders and they may be evoked by the actions taken by other cannot all of the empirical findings that10 M. been reported depict stock markets; nearly see the potential price at which have EUR could be traded. Nevertheless, market participants2 . Static models do not account for the casual effects such as traders have thefew exceptions observing the continually changing priceet al. (2005), possibility of all of the there arespill-overs between of devoted rates of various order types exist. Moreover, possible only a the arrival to currency trading (Bloomfeld executed transactions with corresponding indicators "P" or "T". This allows them Lo & Sappof the empirical findings that have been reported depict stock markets; nearly all (2008)). to deduce whether the trade was "Paid" (initiated by an ask side, hence a market there are only a few exceptions devoted to currency trading (Bloomfeld et al. (2005), sell) or "Taken" (initiated by a bid side, henceforth a market buy). Although the Lo 3 & Sapp (2008)). is Data exact Market and not able to be seen, market participants can gain a certain volume of trades intuition about the changes in the order flow via the observed quantities of executed The FX market of the Polish Zloty is the most liquid among all the currency markets 3 theMarket and emerging economies3. Spot transactions can be executed Data orders. of Central European on the OTC market using the Reuters Dealing Direct system, via submitted to the The FX market of thethis study comprise market and limit all the currency markets datasets used in Polish Zloty is the most liquid among orders a voice broker or by the or cancelled from the all trades is conducted transactions can be executed of telephone. European of market between Jan 2007 and 31 Jan 2007. The systemCentral About halfemerging economies3 . 2Spot via the Reuters Dealing 3000 Spot Matching System (RDSMS) and the quantity of of this platformEuro. During on the OTC market rate the Reuters a importance system, via a is continually EUR/PLN exchangeusing is quoted as Dealing DirectZlotys per onevoice broker or by period pronounced inhalf of all tradesmarkets where, based uponReuters Dealing 3000 the telephone.study, thethe automated FXan appreciatingvia thetowards Euro. Trading This is most of About Zloty followed is conducted trend the information obtained SpotFX dealers, about 80% place within the speculative of(i.e. London banks) as well of the Polish Zloty takes of trades are purelyimportancein their motivation. is continually from Matching System (RDSMS) and offshore markets this platform The remainder are motivated by real trading datasets cover both of these trading venues. Every order as within Poland4 and theneeds. 2 3 This is most pronounced in the automated FX markets where, based upon the information obtained According to the survey of FX market activity conducted by the Bank for International Settlements includes an exact date and time of submission as well as an execution/cancellation from FX dealers, about daily turnover in purely speculative in their amounted The remainder BIS (2007), the average 80% of trades are interbank spot transactionsmotivation. to 4,851 million indicator, a 2007. This market is, and an indicator for the market side spotamarket for the are motivated by real trading size therefore, nearly two times bigger than the of quote. The USD in April firm quote, a needs. 3 According to the survey the average daily turnover amounted Bank for International Aprilbook detailed structure of of FXdatasets makes it possibletheto 2,959 million USD inSettlements Hungarian Forint where the market activity conducted by to rebuild the entire order 2007 BIS about three average daily activity.the figure 3spot transactions amounted to state million and (2007), the times more liquid than interbank the Czech the exemplary 4,851 of the at each moment of market turnover inIn market forwe presentKoruna (1,630 million USD). USD in April 2007. This market is, therefore, nearly two times bigger than the spot market for the order book on 18 January, 16:13 CET. In this particular snapshot, the whole depth Hungarian Forint where the average daily turnover amounted to 2,959 million USD in April 2007 8

2

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4

and about three times more liquid than the market for the Czech Koruna (1,630 million USD). About 80% of the turnover takes place in the offshore market and a l remaining o f P o tradesd 20% are l a n N a t i o n the B a n k between banks located within Poland. 8

9

orders.

Market and Data

The datasets used in this study comprise market and limit orders submitted to the system or cancelled from the market between 2 Jan 2007 and 31 Jan 2007. The EUR/PLN exchange rate is quoted as a quantity of Zlotys per one Euro. During the period of study, the Zloty followed an appreciating trend towards Euro. Trading of the Polish Zloty takes place within offshore markets (i.e. London banks) as well as within Poland4 and the datasets cover both of these trading venues. Every order includes an exact date and time of submission as well as an execution/cancellation indicator, a the quote, a size and It indicator for the market side of a quote. The growing overfirm subsequent years. an is a very liquid and transparent electronic brodetailed structure side (sell limit orders) amounts to22 M. EUR entire orderat the on the system, operating as an order-driven market rebuild automatically book kerage ask market of the datasets makes it possibleto that can the (the depth match at each moment visible to traders their 2 M. EUR) whereas the can submit of bid best ask buy and market activity. In figure 3 agree. FX dealers depth on the the incomingthat is of sell orders once equalsprices we present the exemplary state either order book (buy January, 16:13 CET.are this particular snapshot, best bidand agmarket market orders; market orders In perceived as liquidity-consuming depth limit or sideon 18 limit orders) equals 15 M. EUR (the depth at thethe wholethat is on the to traders equals(sell limit orders) amounts to 22 M. EUR (the limit at the visible ask market are 2 M. EUR). gressive since they side immediately executed against most competitivedepth orders About 80% of the turnover to traders in the offshore EUR) whereasremaining 20% are trades best ask that is visible takes the equals 2 M. of the system is concerned, traders in the order book. As far asplace transparency market and the the depth on the bid Although trading on the interbank market can take place 24 at day bid 7 days between banks(buy limit orders) equals 15 M. EUR (the depthhours a best and that is market side located within Poland. can observe continually changing best ask and bid prices thatthe correspond to the a week,to traders visible it is heavily concentrated on working days between 8:00 and 18:00 Central most competitive equals 2 M. EUR).orders stored in the order book. They can also buy and sell limit 9 European Time (GMT+1, with Daylight Savings Time). The amount of orders see the whole size of best ask and best bid limit orders (the depth at the best ask Although trading on the interbank market can negligible (seehours a 3). In order to submitted beyond these time frames is quite take place 24 figure day and 7 days and the depth at the best bid) but only if this size does not exceed 10 M. EUR. a week, itundesired impact of periods working days between 8:00 and 18:00 exclude limit the is heavily concentrated on where trading is particularly thin, we Central If it is the case, the quantity of the whole depth is hidden and the sign "R" (reguEuropean Time (GMT+1, weekends and on working days between 18:00 of orders observations registered on with Daylight Savings Time). The amount and 8:00 lar order) appears next to the best ask or the best bid quotation. Such a solution submitted beyond these time frames is quite negligible (see figure 3). In order to CET5 . allows for the size of large orders submitted to the system at the best prices to be limit the undesired impact of periods where trading is particularly thin, we exclude hidden. Traders can see neither the price nor the quantity of all other (less competobservations registered on weekends and on working days between 18:00 and 8:00 itive)5 orders placed in the system. Unlike the EUR/USD currency pair, traders also CET . cannot see the potential price at which 10 M. EUR could be traded. Nevertheless, traders have the possibility of observing the continually changing price of all of the executed transactions with corresponding indicators "P" or "T". This allows them to deduce whether the trade was "Paid" (initiated by an ask side, hence a market sell) or "Taken" (initiated by a bid side, henceforth a market buy). Although the exact volume of trades is not able to be seen, market participants can gain a certain intuition about the changes in the order flow via the observed quantities of executed orders.

4

3

The datasets used in this study comprise market and limit orders submitted to the Figure 1: A snapshot of the market for the EUR/PLN currency 31 The stepwise lines system or cancelled fromthe order book between 2 Jan 2007 and pair. Jan 2007. The depict the ask (upper line) and bid (lower line) slope curves. EUR/PLN exchange rate is quoted as a quantity of Zlotys per one Euro. During the period of study, the Zloty followed an appreciating trend towards Euro. Trading 1: snapshot of ofFigure 2: Intraday takes the order book offshoreEUR/PLN (i.e. Londoncancellations well the PolishAZloty frequency of within for the markets currency pair. banks) as (right place order submissions (left panel) and order The stepwise lines Figure depict the ask (upper line) and bid (lower line) slope curves. panel). as within Poland4 and the datasets cover both of these trading venues. Every order includes an exact date and time of submission as well as an execution/cancellation All of the incoming orders size and ancategorized according to their of a quote. The indicator, a firm quote, a have been indicator for the market side level of aggressiveness as in the studies datasets & Hautsch (2006) to rebuild theal. (2007). Inbook detailed structure of the of Hall makes it possible and Ellul et entire order the analysis momentincluded cancellations of best3buy present the exemplaryOur sample at each we also of market activity. In figure we and sell limit orders. state of the covers book on 18 January, 16:13 CET.of them particular snapshot,ten categories: order 92,818 selected events and each In this fall into the one of the whole depth

4

About 80% of the turnover takes place in the offshore market and the remaining 20% are trades order; located within Poland. between banksin this case the price of the incoming sell order is lower or equal to 5 the most competitive bid price prevailing in the order book. Such orders A similar truncation procedure has also been performedin the study of Lo & Sapp (2008). are

· k = 1 (MS) ­ Submission of a market sell order or a marketable limit sell

9 immediately executed against the limit orders stored on the bid side of the 10 submissions in the sample. order book. There are 10,808 MS order

A similar truncation WORKING PAPER No. 104

5

· k = 2 (IQS)­ Submission of an inside-the-quote limit sell order; in this case the price of the incoming sell order 10lower than the best ask price but higher is than the best bid price. Such orders improve the best ask price. There are

procedure has also been performed in the study of Lo & Sapp (2008).

13

All of the incoming orders have been categorized according to their level of aggressiveness as in the studies of Hall & Hautsch (2006) and Ellul et al. (2007). In the analysis we also included cancellations of best buy and sell limit orders. Our sample covers 92,818 selected events and each of them fall into the one of ten categories:

Market and Data

3

· k = 1 (MS) ­ Submission of a market sell order or a marketable limit sell order; in this case the price of the incoming sell order is lower or equal to the most competitive bid price prevailing in the order book. Such orders are immediately executed against the limit orders stored on the bid side of the order book. There are 10,808 MS order submissions in the sample. · k = 5 (CS) ­ Cancellation of an inside-the-quote or an at-the-quote limit sell · k = 2 (IQS)­ are 7,429 CSof an inside-the-quote . limit sell order; in this case order. There Submission events in the sample6 the price of the incoming sell order is lower than the best ask price but higher · than the best ­ Submission of a market buy order best ask price. There buy k = 6 (MB) bid price. Such orders improve the or a marketable limit are order; in this case the price of the incoming 14,395 IQS order submissions in the sample. buy order is greater then or equal to the lowest (most competitive) ask price in the order book. Such orders are · k = 3 (AQS) ­ Submission of an at-the-quote limit sell order; sidethis the order immediately executed against limit orders stored on the ask in of case the price ofThere are 11,069 MB orderequal to the best ask price prevailing in the book. the incoming sell order is submissions. system. These orders increase the depth at the best ask. There are 4,871 AQS · order7submissions in the sample. inside-the-quote limit buy order; in this case k = (IQB) ­ Submission of an the price of the incoming buy order is lower than the best ask price but is · k = 4 (BQS)theSubmission of a Such orders improve the best bid price. There higher than ­ best bid price. behind-the-quote limit sell order; in this case the price ofIQB order submissions. than the lowest (most competitive) ask are 14,239 the sell order is higher price in the order book. There are 9,308 BQS order submissions in the sample. · k = 8 (AQB) ­ Submission of an at-the-quote limit buy order; in this case the · price5of the incoming buy order isinside-the-quote orof the best buy limit order k = (CS) ­ Cancellation of an equal to the price an at-the-quote limit sell prevailing in the book. CS events in increase the .depth at the best bid. There order. There are 7,429 Such orders the sample6 11 are 4,231 AQB order submissions. · k = 6 (MB) ­ Submission of a market buy order or a marketable limit buy · k = 9 (BQB) case the price of a behind-the-quote limitis greater then thisequal order; in this ­ Submission the incoming buy order buy order; in or case thethe lowest (most competitive) ask price in the the best bid price. orders are to price of the incoming buy order is lower than order book. Such There 9,188 BQB order submissions. limit orders stored on the ask side of the order immediately executed against book. There are 11,069 MB order submissions. · k = 10 (CB) ­ Cancellation of an inside-the-quote or an at-the-quote limit buy · order. (IQB) ­ Submission of an inside-the-quote limit buy order; in this case k = 7 There are 7,280 CB events in the sample.

4

the price of the incoming buy order is lower than the best ask price but is higher The than the best bid price. Such orders improve the best bid price. There Econometric Approach are 14,239 IQB order submissions.

In a very close analogy to Bauwens & Giot (2003), we consider the model for the · k = 8 (AQB) ­ Submission of an at-the-quote limit buy order; in this case the marked point process {xi , yi }, where xi = ti -ti-1 is a duration between the moments price of the incoming buy order is equal to the price of the best buy limit order in which subsequent orders arrive to the system or are withdrawn from it and yi is prevailing in the book. Such orders increase the depth at the best bid. There an indicator variable for a particular type of an event yi = k (where k = 1, 2, ..., 10)7 . are 4,231 AQB order submissions.

6

We include cancellations of best limit sell and best limit ask orders since they are believed to have · k = 9 (BQB) ­ Submission of a behind-the-quote limit buy order; in this case greater informational content then cancellations of behind-the-quote orders. In this way we do not the price of the incoming buy order is lower than the best bid price. There are cover cancellations of orders that have "moved away" from the market price and were perhaps left in the 9,188 BQB very long time. Their removal from the system does not bring much insight system for a order submissions. into either the process of price formation or liquidity provision in comparison to the behavior of best· k = 10 (CB) ­ Cancellation of an inside-the-quote or an at-the-quote limit buy limit orders. 7 Although a subset of natural CB eventsisin applied to define a discrete process yi order. There are 7,280 numbers the sample. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, the numbers are used as qualitative indicators in order to discriminate

14

4

N a 12 The Econometric Approacht i o n a l

B a n k

o f

P o l a n d

In a very close analogy to Bauwens & Giot (2003), we consider the model for the

are 14,239 IQB order submissions.

Market and Data

· k = 8 (AQB) ­ Submission of an at-the-quote limit buy order; in this case the price of the incoming buy order is equal to the price of the best buy limit order prevailing in the book. Such orders increase the depth at the best bid. There are 4,231 AQB order submissions. · k = 9 (BQB) ­ Submission of a behind-the-quote limit buy order; in this case the price of the incoming buy order is lower than the best bid price. There are 9,188 BQB order submissions. · k = 10 (CB) ­ Cancellation of an inside-the-quote or an at-the-quote limit buy order. There are 7,280 CB events in the sample.

4

The Econometric Approach

In a very close analogy to Bauwens & Giot (2003), we consider the model for the marked point process {xi , yi }, where xi = ti -ti-1 is a duration between the moments in which subsequent orders arrive to the system or are withdrawn from it and yi is an indicator variable for a particular type of an event yi = k (where k = 1, 2, ..., 10)7 .

6

3

We include cancellations of best limit sell and best limit ask orders since they are believed to have greater informational content then cancellations of behind-the-quote orders. In this way we do not cover cancellations of orders that have "moved away" from the market price and were perhaps left in the system for a very long time. Their removal from the system does not bring much insight into either the process of price formation or liquidity provision in comparison to the behavior of best limit orders. 7 Although 2: Intradayof natural of order submissions (left panel) and discrete process yi(right Figure a subset frequency numbers is applied to define a order cancellations {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, the numbers are used as qualitative indicators in order to discriminate panel).

12 All of the incoming orders have been categorized according to their level of aggressiveness as in the studies of Hall & Hautsch (2006) and Ellul et al. (2007). In the analysis we also included cancellations of best buy and sell limit orders. Our sample covers 92,818 selected events and each of them fall into the one of ten categories: · k = 1 (MS) ­ Submission of a market sell order or a marketable limit sell order; in this case the price of the incoming sell order is lower or equal to the most competitive bid price prevailing in the order book. Such orders are immediately executed against the limit orders stored on the bid side of the order book. There are 10,808 MS order submissions in the sample. · k = 2 (IQS)­ Submission of an inside-the-quote limit sell order; in this case the price of the incoming sell order is lower than the best ask price but higher than the best bid price. Such orders improve the best ask price. There are 14,395 IQS order submissions in the sample. · k = 3 (AQS) ­ Submission of an at-the-quote limit sell order; in this case the price of the incoming sell order is equal to the best ask price prevailing in the system. These orders increase the depth at the best ask. There are 4,871 AQS order submissions in the sample. · k = 4 (BQS) ­ Submission of a behind-the-quote limit sell order; in this case the price of the sell order is higher than the lowest (most competitive) ask WORKING PAPER No. 104 price in the order book. There are 9,308 BQS order submissions in the sample.

15

the price of the incoming buy order is lower than the best bid price. There are The Econometric Approach 9,188 BQB order submissions. · k = 10 (CB) ­ Cancellation of an inside-the-quote or an at-the-quote limit buy order. There are 7,280 CB events in the sample.

· k = 5 (CS) ­ Cancellation of an inside-the-quote or an at-the-quote limit sell order. There are 7,429 CS events Giot sample6 . In a very close analogy to Bauwens & in the(2003), we consider the model for the marked = 6 (MB) ­ Submission of a imarket i-1 is order or a between the limit buy · k point process {xi , yi }, where x = ti -t buy a duration marketable moments in which subsequent orders arriveofof theincomingor are withdrawn from itBQS, yi is At the end of each duration price tothe system buy order is IQS, AQS, andequal order; in this case the xi one ten possible states: MS, greater then or CS, 7 an indicator lowest (most CB can be type ofprice in the = k (where kSuch orders are MB, IQB, AQB, BQB or competitive) ask an event yi orderxbook. be treated as an to the variable for a particular observed. Accordingly, i can = 1, 2, ..., 10) . · k = 5 (CS) ­ Cancellation of an inside-the-quote or an at-the-quote limit sell At the end of each executed againstof min(xi,1 , xi,2 , states: ),the IQS,each of BQS, CS, ten x where AQS, variables outcome variable of a function one=limit possible ..., 6 i,10 MS, ask side of the order immediately duration xi xi 6 order. There are best limit events in orders stored on the sample . We include cancellations of7,429 CS sell and best limit ask orders since they are believed to have MB, IQB, AQB, BQB or CB MB order submissions. 1, 2, ..., 10) corresponds observed. Accordingly, xi would treated as an xi,k (for k =There are 11,069 can be to an order duration that can be end up in the greaterbook. informational content then cancellations of behind-the-quote orders. In this way we do not x ), marketable variables outcome=variable orders that framework away" buy ..., market amodel, only perhapsbuy · k 6 (MB) ­ Submission = min(x competing risks price and were limit left state cancellations ofof a function x"moved of ai,1 ,from, the xi,10or where each ofthe shortcover k. As in the standard have iof a market i,2 order xi,k ·(for k 7 in this case corresponds the an (realized), orderdoes would if in thisequal order; 1, a ..., long time. Their to incomingthe system buy order; much the estthe k =ten(IQB) ­ 10) the priceofobservedorder duration that greater end up incase in from = for 2, verySubmissionis ofan inside-the-quotewhichis not bring an or insight system possible durations removal from buy limit happens then order of the the process of price formation order is provision risks it. For price shortinto eitherAs lowest (most competitive) of is cancelledorder book. Such the but is state k. the in the the enters frameworkliquidity lowerthe infrommodel,askthe orders if of to price type incoming system or competing the best only behavior a a correspondingof standard the buyor askaprice in than comparison to example, are best higher possible best bid is observedorders improve the ask bidifof the est from orders. 1)the durationsprice.limit MS duration which happensobservedThere an order ti . immediately were posted, only the (realized), on would be at of MS limit tenithan executed against Suchorders stored xi,1 the best side price. order order (y = 7 Although a subset of natural numbers is applied to define a discrete process yi a corresponding that would submissions.up in other states (i.e. it. For example, CS, book. There are enters the system or is cancelled from IQS, AQS, BQS, if a Otherare 14,239 IQB order have ended submissions. durations type 11,069 MB order

4

The Econometric Approach

4

observed at ti . MS order (yi = 1) wereand CB durations) would be therefore unobservable and are MB, IQB, 8AQB, BQB posted, only the MS duration xi,1 would be in this case the · k = 7 (AQB) ­ Submission of an inside-the-quote limit buy order; in this case · k = (IQB) ­ Submission of an at-the-quote limit buy order; Other durations that wouldarrivalended up in order at time(i.e. IQS, AQS, BQS, CS, have of treated as censored by the buy order the 12 to the states ofti . best buy limit order MS other price of the incoming the price of the incoming buy is equal lower price the best ask price but is order is than the MB, IQB, AQB, BQB and CB durations) would be therefore unobservable and are higher than the book. Such orders orders the depth at the best bid. There As in prevailing inthe best bid price. Suchincreaseimprove the best bid price. There the censored by the arrival competing risks model, i . treated as standard framework of aof the MS order at time twe consider a joint conarebivariateIQB order submissions. are 4,231 AQB order submissions. ditional 14,239 density for xi and yi 8 : As in the standard framework of a competing risks model, we consider a joint con· k = 9 (AQB) ­ Submission of anbehind-the-quote limit buy order;this this case · k = 8 (BQB) ­ Submission of a108at-the-quote I k limit buy order; in in case the ditional bivariate f (xi , yi |Fi-1xi and yi :hxk (xi |Fi-1 ) i Sxk (xi |Fi-1 ) density for ) = (1) the price of incoming buy buy order is lower than the best bid price.limit order price of the the incoming orderk=1 equal to the price of the best buy There are is 10 9,188 BQB order book. Such orders increase the depth at the best bid. There k prevailing in the submissions. k (1) yi |Fi-1 ) = f (xi , variable (Iik = 1 hxk (xi |Fi-1 i I= kk (xiobserved at time ti and if a state y) i Sx is |Fi-1 ) where I is a dummy are 4,231 AQB order submissions. k=1 · k = 10 (CB) Cancellation of an inside-the-quote or an an information set up Iik = 0 if a state yi­= k is observed at time ti ). Fi-1 denotes at-the-quote limit buy k k whereorder. (BQB) 1 that contains past realizationsi of xilimit buyhorder; time denote to a time point t - are variable (Ievents if a state y = k and yi , xk and inxthisi case · kI= is a dummySubmission iof= 1 in the sample. is observed at S k t and 9 There ­ 7,280 CB a behind-the-quote k Ii hazard and aof yi = incoming buy orderrespectively. denotes an information set are a = 0 if a statesurvival is observed at ktime lower than the best bid price. There up the price the k function for x , is ti ). Fi-1 to 1 9,188 4 a time point t - is that contains past realizations of xi and yi, hxk and Sxk denote TheBQB order submissions. contributes The duration Econometric Approach to the joint conditional density that realized (observed) respectively. a hazard and a survival function for xk , · k = 10 (CB) equation (1) of its density function, an at-the-quote limit buy function given by ­ Cancellationvia an inside-the-quote or whereas other unrealized In a very close analogy to Bauwens & Giot (2003), we consider the model for the The duration that is realized CB to it via contributes to the joint conditional density order. There are 7,280 (observed) their survival (censored) durations contribute events in the sample. functions. For example, if a marked point process {xi , yi }, where xi = ti -ti-1 is a duration between the moments function given by equation the conditional bivariate density of the pair unrealized state MS is observed at ti , (1) via its density function, whereas other {xi , yi } is in which subsequent orders arrive to the system or are withdrawn from it and yi is (censored) durations contribute to it via their survival functions. For example, if 7a given by: an The Econometric type of an event i = k (where k 4 indicator variable for at particularApproach ydensity of the = 1, 2, ...,y10)is. pair {xi , i } state MS is observed at i , the conditional bivariate 10 1 Ii 6 given by: f (x , y = 1|F (2) We a very cancellations ofi-1 ) Bauwens & best ) (2003),|Fi-1 ) they are believed i In include close ianalogy best limit hx1 (xi |Fi-1 limitxask iordersconsiderk (xi |Fi-1 ) for have to = sell and Giot S 1 (x we since Sx the model to the

k=2 greater informational content, then cancellations of -t 10 is a duration between way we do not marked point process {xi yi }, where xi = ti behind-the-quote orders. In thisthe moments 1i-1 10 cover cancellationsi of orders that = hx (xi |Fi-1 )Ii from the market price and|Fi-1 ) have "moved away" Sx (xi |Fi-1 ) were perhaps (2) left 1 in which f (xi , y = 1|Fi-1 ) arrivex1 (xthei-1 ) subsequent orders = f 1 i |F systemSor (xi |Fi-1 ) Sxk (xfrom it and yi is to are withdrawn i xk in the system for a very long time. Their removal from the system k=2 not bring much insight does k=2 an either the process for a formation type of an event y = k (where = 1, behavior 7 . 10 intoindicator variableof priceparticular or liquidity provisioni in comparisonkto the 2, ..., 10)of best limit orders. duration xi = fx1with an )MS Sxk (xi |Fi-1= 1), xi contributes to (xi |Fi-1 ends order (yi ) Therefore, if a 6 7 We include cancellations of best limit sell and best limit ask orders since they are believed to have Although a subset of natural numbers is applied to define a discrete process yi k=2 the density function via:then cancellations of behind-the-quote orders. In this way we do i.e. (1) the conditional density of xi,1 evaluated at xi , not greater informational content {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, the numbers are used as qualitative indicators in order to discriminate = 1), xi contributes to Therefore, if a durationthat have "moved away" from the market price and were perhaps left x ends with an cover cancellations of orders natural ordering of yk MS order (yany informative meaning in the selected events. Accordingly, i does not have i the density for a very long time. the conditional density of xi,1 evaluatedmuchxinsight in the system model. 12 context of this function via: (1) Their removal from the system does not bring at i , i.e. 8 The model the process of price formation or liquidityi-1 ) between comparison i,1 , xi,2 , behavior of into either assumes independence (conditionally on F provision in durations x to the ..., xi,10 . selected events. Accordingly, natural ordering of yk does not have any informative meaning in the best limit orders. context of this model. 7 applied to define a discrete process yi 8 Although a subset of natural numbers is 13 The model assumes independence (conditionally on Fi-1 ) between durations xi,1 , xi,2 , ..., xi,10 . {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, the numbers are used as qualitative indicators in order to discriminate

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, the numbers are used as qualitative indicators in order to discriminate

16

13 12

N a t i o n a l

B a n k

o f

P o l a n d

function given by equation (1) via its density function, whereas other unrealized (censored) durations contribute to it via their survival functions. For example, if a The Econometric Approach state MS is observed at ti , the conditional bivariate density of the pair {xi , yi } is given by:

10

f (xi , yi = 1|Fi-1 ) = hx1 (xi |Fi-1 ) Sx1 (xi |Fi-1 )

k=2 10

1 Ii

Sxk (xi |Fi-1 )

(2)

= fx1 (xi |Fi-1 )

k=2

Sxk (xi |Fi-1 )

Therefore, if a duration xi ends with an MS order (yi = 1), x contributes to fx1 (xi |Fi-1 ) and (2) the joint conditional probability that all otheri unobserved duthe density function via: (1) the conditional density of xi,1 evaluated at xi , i.e. rations xi,k (with end states k = 2, ..., 10) are longer than the realized duration xi : 10 |Fi-1 and (2) fx1 (xiS events. Accordingly, joint conditional yk does not have any informative meaning induselected xk (x) |Fi-1 ). the natural ordering of probability that all other unobserved the i k=2 rations of i,k (with end states k = 2, ..., 10) are longer than the realized duration xi : context x this model. 8 10 The conditional hazard and (conditionally on Fi-1 ) between durations xi,1 ,durations x assumes independence survival functions for each of selected xi,2 , ..., xi,10 . The model(xi |Fi-1 ). i,k k=2 Sxk are specified with the Logarithmic ACD models with a Weibull distribution of an 13 The conditional Bauwensand Giot (2000)). The for each of selected durations xi,k error term (see hazard & survival functions conditional duration expectations are specified in a dynamic fashion, such as previous states and previously observed are specified with the Logarithmic ACD models with a Weibull distribution of an error term (see exert an influence on their length.conditional duration expectations durations could Bauwens & Giot (2000)). The In the standard framework of the are specified x ais given as: ACD model in dynamic fashion, such as previous states and previously observed i,k durations could exert an influence on their length. In the standard framework of the (3) xi,k = i,k i,k ACD model xi,k is given as: where i,k = i,k · i,k = xi,k = i,k i,k and µi is the mean of the Wiebull E(xi,k |Fi-1 ) (3) 9 distribution , i,k is a Weibull-distributed error term (i,k i.i.d. W (k , 1), where -1 where i,k = parameter ,and a = E(xi,k |Fparameter is restricted to 1). the Wiebull k is a shape i,k · µi i,k dispersion i-1 ) and µi is the mean of Conditional distribution9 , to Fis a duration expectations are modelled with the Log-ACD model (with respect i,k i-1 ) Weibull-distributed error term (i,k i.i.d. W (k , 1), where k is a I10 . The logarithms of dispersion parameter restricted to 1). of type shape parameter and a duration expectations is i,k = ln(i,k ) are: Conditional (with respect to Fi-1 ) duration expectations are modelled with the Log-ACD model 10 of type I10 . The logarithms of duration expectations i,k = ln(i,k ) are: l i,k = (l,k + l,k ln xi-1 )Ii-1 + k i-1,k (4) µ-1 , i i,k = =

l=1 10 10 l (l,k + l,k ln xi-1 )Ii-1 + k i-1,k l l=1 (l,k + l,k ln xi-1,l )Ii-1 + k i-1,k l=1 10 l = (l,k + ln xi-1,l )Ii-1 + k i-1,k where l = 1, 2, ..., 10 and Iil is a dummy l,k indicator (Iil = 1, if a state yi = l at the end l=1 of duration xi and Iil = 0, if yi = l ). where l = 1, 2, ..., 10 and Iil is a dummy indicator (Iil = 1, if a state yi = l at the end The econometric specifications of ). of duration xi and Iil = 0, if yi = lduration expectations according to the previously realized state of yi . Thus, the expected waiting times till particular order submisThe or cancellations will take place vary expectations of the previously observed sionseconometric specifications of duration with the typeaccording to the previously realized state time Thus, the expected waiting times till events and theof yi . that had elapsed until they occurred. particular order submissions or cancellations will take place vary with the type of the previously observed Assuming the time that had elapsed until error terms events and the Weibull distribution for thethey occurred.i,k , the joint conditional density function for the pair {xi , yi } can be derived as: Assuming the Weibull distribution for the error termsk i,k , the joint conditional k Ii x } density function for the pair {xi , yi10 can k derived -1 - i be xi k as: i,k f (xi , yi |Fi-1 ) = (5) ·e i,k i,k k k Ii k=1 10 -1 x - i xi k k i,k (5) · eof the MAACD model were f (xi , yi |Fi-1 ) = 9 An exposition of the Weibull distribution and some major properties i,k i,k k=1

4

(4)

provided in the Appendix. properties of the Log-ACD models can be major properties Galli MAACD model An exposition of the Weibull distribution and somefound in Bauwens,of the & Giot (2008). were provided in the Appendix. 10 Detailed properties of the Log-ACD models can14 found in Bauwens, Galli & Giot (2008). be

10 9 Detailed

WORKING PAPER No. 104

14

17

realized state of yi . Thus, the expected waiting times till particular order submisThe Econometric Approach sions or cancellations will take place vary with the type of the previously observed events and the time that had elapsed until they occurred. Assuming the Weibull distribution for the error terms i,k , the joint conditional density function for the pair {xi , yi } can be derived as:

10

f (xi , yi |Fi-1 ) =

k=1

9

xi k i,k i,k

k k -1 Ii

·e

-

xi i,k

k

(5)

An exposition of the Weibull distribution and some major properties of the MAACD model were provided in the Appendix. Accordingly, the joint log-likelihood function can be given as the sum of ten log10 Detailed properties of the Log-ACD models can be found in Bauwens, Galli & Giot (2008).

likelihoods:

10

ln L(|xi , yi , Fi-1 ) =

k=1 10

14 ln Lk (k |xi , yi , Fi-1 ) Iik ln xi k i,k i,k

k -1 10

(6) -

k=1

=

k=1

xi i,k

k

4

where = k , k = {l,k , l,k , k , k } (for l = 1, 2, ..., 10). Because there are no relations between the parameters from the distinct subsets k (as durations xi,k are independent conditionally on Fi-1 ), we are able to estimate the model by separately maximizing ten log-likelihoods: ln Lk (k |xi , yi , Fi-1 ). The proposed specification of the MAACD model is very complex and demands very rich parametrization. In fact, we allow for 220 different parameters (i.e. 22 parameters for each of ten possible states). But this generality does not come at a cost of a burdensome estimation process. The real advantage of the model is that the estimation is very fast and easy if we profit from the decomposition of the likelihood function.

5

The Empirical Application

The intraday activity of the process of order submissions experiences very strong intraday seasonality (see Figure 2). We assume the multiplicative diurnality pattern and then, we model the deseasonalized variable xi = xti using the MAACD specifica¯ s tion. The intraday seasonality factor st is derived by the nonparametric method. We apply kernel regression of durations on a time-of-day variable as has been proposed in Bauwens & Veredas (2004): s(t) =

T t-ti i=1 K h T K t-ti i=1 h

xi

(7)

where K is the quartic kernel function, h is the optimal bandwidth selected as 1 2.78sN - 5 (s is the standard deviation of the data), N is the number of observations and ti is a time-of-day variable standardized on the [0,1] interval (i.e. a cumulative number of seconds from 8.00 CET until the moment of the order submission and then divided by the number of seconds in each day). Using the deseasonalized series xi and the corresponding yi indicators, we estimated ¯ the MAACD model with separate maximizing ten components of the log likelihood function given by the formula 6. We used the BHHH optimization algorithm from 15

18

N a t i o n a l B a n k o f P o l a n d

the MAACD model is very complex and demands very rich parametrization. In fact, we allow for 220 different parameters (i.e. 22 parameters for each of ten possible The Empirical Application states). But this generality does not come at a cost of a burdensome estimation process. The real advantage of the model is that the estimation is very fast and easy if we profit from the decomposition of the likelihood function.

5

The Empirical Application

The intraday activity of the process of order submissions experiences very strong intraday seasonality (see Figure 2). We assume the multiplicative diurnality pattern and then, we model the deseasonalized variable xi = xti using the MAACD specifica¯ s tion. The intraday seasonality factor st is derived by the nonparametric method. We apply kernel regression of durations on a time-of-day variable as has been proposed in Bauwens & Veredas (2004): s(t) =

T t-ti i=1 K h T K t-ti i=1 h

xi

(7)

where K is the quartic kernel function, h is the optimal bandwidth selected as 1 2.78sN - 5 (s is the standard deviation of the data), N is the number of observations and ti is a time-of-day variable standardized on the [0,1] interval (i.e. a cumulative number of seconds from 8.00 CET until the moment of the order submission and then divided by the number of seconds in each day). Using the deseasonalized series xi and the corresponding yi indicators, we estimated ¯ the MAACD model with separate maximizing ten components of the log likelihood function given by the formula 6. We used the BHHH optimization algorithm from the maxlik library of Gauss 10.0. The parameter estimates and their corresponding 15 p-values (corresponding to the standard errors computed with a robust "sandwich" formula) are presented in Table 1. All variables that are responsible for dynamic features of the MAACD model are statistically significant, which confirms strong auto and crosscorrelations among time periods elapsing to different orders. Each of the main columns in the upper and lower panels of the table contain parameter estimates that describe the conditional expectation of a duration that ends as one of the ten possible outcomes. For example, in the first column of the upper panel of the table we show estimates of equation 4 for the duration expectation that elapses with the arrival of the MS order. Analogously, the second column of the lower panel of the table presents estimates of the conditional expected duration that elapses if an IQB order is posted in the system. Different intercepts (i.e. l,k ) correspond ^ to various reactions of the expected duration to the preceding event, whereas l,k ^ ^k estimates are responsible for the scale of duration clustering. The clustering and effect may also vary according to the previous state because we allow for different l,k coefficients for the past duration, conditional on the type of a preceding order. ^

5

WORKING PAPER No. 104

19

The Empirical Application

5

I. ASK SIDE OF THE MARKET (SELL ORDERS) MS, k=1 IQS, k=2 AQS, k=3 BQS, k=4 parameters estimate p - value estimate p - value estimate p - value estimate p - value 1,k MS -0.0437 0.0539 I. ASK SIDE OF THE MARKET (SELL ORDERS) 0.6665 0.0000 0.5988 0.0000 0.5437 0.0000 2,k IQS 0.6044 k=1 0.0000 1.2937 k=20.0000 0.4715 0.0000 0.4570 0.0000 MS, IQS, AQS, k=3 BQS, k=4 3,k AQS estimate 0.4858 p - 0.0000 0.9437 0.2432 0.5662 parameters value estimate p -0.0000 value estimate p 0.0001 - value estimate p 0.0000 - value BQS 0.8061 0.0000 1.1856 0.0000 0.7460 0.0000 0.2791 0.0000 1,k4,k MS -0.0437 0.0539 0.6665 0.0000 0.5988 0.0000 0.5437 0.0000 CS 0.8260 0.0000 -0.0784 0.0000 0.5894 0.0000 0.5341 0.0000 IQS 0.6044 0.0000 1.2937 0.0000 0.4715 0.0000 0.4570 0.0000 2,k5,k MB 0.5240 0.0000 0.1420 0.0000 0.4005 0.0000 0.1479 0.0000 AQS 0.4858 0.0000 0.9437 0.0000 0.2432 0.0001 0.5662 0.0000 3,k6,k IQB 0.8512 0.0000 1.1050 0.0000 0.8605 0.0000 0.5094 0.0000 BQS 0.8061 0.0000 1.1856 0.0000 0.7460 0.0000 0.2791 0.0000 4,k7,k 8,k AQB 0.6912 0.0000 1.2293 0.0000 0.7605 0.0000 0.4827 0.0000 0.8260 0.0000 -0.0784 0.0000 0.5894 0.0000 0.5341 0.0000 5,k CS BQB 0.8512 0.0000 1.1436 0.0000 0.8629 0.0000 0.6585 0.0000 6,k9,k MB 0.5240 0.0000 0.1420 0.0000 0.4005 0.0000 0.1479 0.0000 10,k CB 0.6912 0.0000 0.9714 0.0000 0.9284 0.0000 0.6396 0.0000 0.8512 0.0000 1.1050 0.0000 0.8605 0.0000 0.5094 0.0000 7,k IQB 0.8256 0.0000 0.6862 0.0000 0.8573 0.0000 0.8732 0.0000 0.6912 0.0000 1.2293 0.0000 0.7605 0.0000 0.4827 0.0000 8,kk AQB MS 0.1120 0.0000 0.1199 0.0000 0.1090 0.0000 0.1004 0.0000 BQB 0.8512 0.0000 1.1436 0.0000 0.8629 0.0000 0.6585 0.0000 9,k1,k 2,k IQS 0.1002 0.0000 0.1732 0.0000 0.1119 0.0000 0.1474 0.0000 10,k CB 0.6912 0.0000 0.9714 0.0000 0.9284 0.0000 0.6396 0.0000 3,k AQS 0.0917 0.0000 0.2173 0.0000 0.1424 0.0000 0.1764 0.0000 0.8256 0.0000 0.6862 0.0000 0.8573 0.0000 0.8732 0.0000 k 4,k BQS 0.1609 0.0000 0.2239 0.0000 0.1854 0.0000 0.1475 0.0000 1,k MS 0.1120 0.0000 0.1199 0.0000 0.1090 0.0000 0.1004 0.0000 5,k CS 0.1411 0.0000 0.1429 0.0000 0.1253 0.0000 0.0740 0.0000 0.1002 0.0000 0.1732 0.0000 0.1119 0.0000 0.1474 0.0000 2,k IQS 6,k MB 0.1266 0.0000 0.0779 0.0000 0.0860 0.0000 0.0374 0.0006 0.0917 0.0000 0.2173 0.0000 0.1424 0.0000 0.1764 0.0000 3,k AQS 7,k IQB 0.1394 0.0000 0.2285 0.0000 0.1382 0.0000 0.1091 0.0000 0.1609 0.0000 0.2239 0.0000 0.1854 0.0000 0.1475 0.0000 4,k BQS 8,k AQB 0.1570 0.0000 0.2428 0.0000 0.1235 0.0001 0.0893 0.0000 5,k9,k BQB CS 0.1411 0.0000 0.1429 0.0000 0.1253 0.0000 0.0740 0.0000 0.1394 0.0000 0.2285 0.0000 0.1682 0.0000 0.1237 0.0000 MB 0.1266 0.0000 0.0779 0.0000 0.0860 0.0000 0.0374 0.0006 6,k10,k CB 0.1570 0.0000 0.2585 0.0000 0.1883 0.0000 0.1559 0.0000 0.1394 0.0000 0.2285 0.0000 0.1382 0.0000 0.1091 0.0000 7,k IQB k 0.7533 0.0000 0.7959 0.0000 0.7897 0.0000 0.7878 0.0000 0.1570 0.0000 0.2428 0.0000 0.1235 0.0001 0.0893 0.0000 8,k AQB 9,k BQB 0.1394 0.0000 0.2285 SIDE OF THE 0.1682 0.0000 0.0000 ORDERS) 0.1237 0.0000 II. BID MARKET (BUY 0.1570 MB, k=6 0.0000 0.2585IQB, k=7 0.0000 0.1883 0.0000 0.1559 0.0000 10,k CB AQB, k=8 BQB, k=9 0.0000 0.7959 0.0000 0.7897 0.0000 0.7878 k parameters 0.7533 estimate p - value estimate p - value estimate p - value estimate p0.0000 - value 1,k MS 1.0270 0.0000 0.1547 0.0000 0.5206 0.0000 0.0657 0.0145 2,k IQS 0.4451 0.0000 II. BID SIDE OF THE MARKET (BUY ORDERS) 1.2617 0.0000 1.0773 0.0000 0.3939 0.0000 MB, IQB, AQB, k=8 BQB, k=9 3,k AQS 0.8078 k=6 0.0000 1.3036 k=7 0.0000 0.9076 0.0000 0.3966 0.0000 4,k BQS estimate 0.7997 p - 0.0000 1.3170 1.1397 0.5467 parameters value estimate p -0.0000 value estimate p 0.0000 - value estimate p 0.0000 - value MS 1.3696 0.0000 1.0206 0.0000 1.1696 0.0000 0.6053 0.0000 1,k5,k CS 1.0270 0.0000 0.1547 0.0000 0.5206 0.0000 0.0657 0.0145 IQS -0.0040 0.8710 0.7478 0.0000 0.8637 0.0000 0.5319 0.4451 0.0000 1.2617 0.0000 1.0773 0.0000 0.3939 0.0000 2,k6,k MB AQS 0.6199 0.0000 1.4317 0.0000 0.6794 0.0000 0.3993 0.0000 0.8078 0.0000 1.3036 0.0000 0.9076 0.0000 0.3966 0.0000 3,k7,k IQB BQS 0.5822 0.0000 1.1176 0.0000 0.5541 0.0000 0.4958 0.0000 4,k8,k AQB 0.7997 0.0000 1.3170 0.0000 1.1397 0.0000 0.5467 0.0000 9,k BQB 0.9516 0.0000 1.3174 0.0000 1.0480 0.0000 0.2266 0.0000 1.3696 0.0000 1.0206 0.0000 1.1696 0.0000 0.6053 0.0000 5,k CS 10,k CB 1.0118 0.0000 -0.1800 0.0000 0.8500 0.0000 0.4308 0.0000 -0.0040 0.8710 0.7478 0.0000 0.8637 0.0000 0.5319 0.0000 6,k MB 0.8024 0.0000 0.6544 0.0000 0.8048 0.0000 0.8919 0.0000 0.6199 0.0000 1.4317 0.0000 0.6794 0.0000 0.3993 0.0000 7,kk IQB AQB 0.2099 0.0000 0.0591 0.0000 0.0424 0.0072 0.0282 0.0033 8,k1,k MS 0.5822 0.0000 1.1176 0.0000 0.5541 0.0000 0.4958 0.0000 BQB 0.1393 0.0000 0.2168 0.0000 0.1669 0.0000 0.0917 0.0000 0.9516 0.0000 1.3174 0.0000 1.0480 0.0000 0.2266 0.0000 9,k2,k IQS 3,k AQS 0.1661 0.0000 0.2385 0.0000 0.1425 0.0000 0.0937 0.0000 1.0118 0.0000 -0.1800 0.0000 0.8500 0.0000 0.4308 0.0000 10,k CB 0.2034 0.0000 0.2358 0.0000 0.1759 0.0000 0.0961 0.0000 k 4,k BQS 0.8024 0.0000 0.6544 0.0000 0.8048 0.0000 0.8919 0.0000 CS 0.1812 0.0000 0.2173 0.0000 0.1699 0.0000 0.1408 0.0000 MS 0.2099 0.0000 0.0591 0.0000 0.0424 0.0072 0.0282 0.0033 1,k5,k 6,k MB 0.1141 0.0000 0.1336 0.0000 0.1157 0.0000 0.1092 0.0000 0.1393 0.0000 0.2168 0.0000 0.1669 0.0000 0.0917 0.0000 2,k IQS 7,k IQB 0.0696 0.0000 0.1473 0.0000 0.1474 0.0000 0.0948 0.0000 3,k AQS 0.1661 0.0000 0.2385 0.0000 0.1425 0.0000 0.0937 0.0000 AQB 0.1279 0.0000 0.2240 0.0000 0.1701 0.0000 0.1658 0.0000 BQS 0.2034 0.0000 0.2358 0.0000 0.1759 0.0000 0.0961 0.0000 4,k8,k BQB 0.2077 0.0000 0.2587 0.0000 0.2022 0.0000 0.1230 0.0000 CS 0.1812 0.0000 0.2173 0.0000 0.1699 0.0000 0.1408 0.0000 5,k9,k CB 0.1913 0.0000 0.1765 0.0000 0.1960 0.0000 0.0471 0.0025 MB 0.1141 0.0000 0.1336 0.0000 0.1157 0.0000 0.1092 0.0000 6,k10,k k 0.7428 0.0000 0.7787 0.0000 0.7833 0.0000 0.7940 0.0000 7,k IQB 0.0696 0.0000 0.1473 0.0000 0.1474 0.0000 0.0948 0.0000 0.1279 0.0000 0.2240 0.0000 0.1701 0.0000 0.1658 0.0000 8,k AQB 0.2077 0.0000 0.2587 0.0000 0.2022 0.0000 0.1230 0.0000 9,k BQB 0.1913 0.0000 0.1765 0.0000 0.1960 0.0000 0.0471 0.0025 10,k CB k 0.7428 0.0000 0.7787 0.0000 0.7833 0.0000 0.7940 0.0000

CS, k=5 estimate p - value 0.4920 0.0000 0.4430 0.0000 CS, k=5 -0.1009 0.0176 estimate p - value 0.9958 0.0000 0.4920 0.0000 0.9454 0.0000 0.4430 0.0000 1.0578 0.0000 -0.1009 0.0176 0.9527 0.0000 0.9958 0.0000 1.0244 0.0000 0.9454 0.0000 1.0939 0.0000 1.0578 0.0000 1.0208 0.0000 0.9527 0.0000 0.7859 0.0000 1.0244 0.0000 0.1007 0.0000 1.0939 0.0000 0.1621 0.0000 1.0208 0.0000 0.1292 0.0000 0.7859 0.0000 0.1509 0.0000 0.1007 0.0000 0.2012 0.0000 0.1621 0.0000 0.1010 0.0000 0.1292 0.0000 0.1421 0.0000 0.1509 0.0000 0.1614 0.0000 0.2012 0.0000 0.1974 0.0000 0.1010 0.0000 0.1044 0.0000 0.1421 0.0000 0.7954 0.0000 0.1614 0.0000 0.1974 0.0000 0.1044 k=10 0.0000 CB, 0.7954 estimate p 0.0000 - value 1.1219 0.0000 1.0776 0.0000 CB, k=10 1.1653 0.0000 1.2018 0.0000 estimate p - value 1.1347 0.0000 1.1219 0.0000 0.6670 0.0000 1.0776 0.0000 0.5209 0.0000 1.1653 0.0000 0.0350 0.4910 1.2018 0.0000 1.2221 0.0000 1.1347 0.0000 1.1967 0.0000 0.6670 0.0000 0.7519 0.0000 0.5209 0.0000 0.1037 0.0000 0.0350 0.4910 0.1782 0.0000 1.2221 0.0000 0.2091 0.0000 1.1967 0.0000 0.1985 0.0000 0.7519 0.0000 0.1519 0.0000 0.1037 0.0000 0.0916 0.0000 0.1782 0.0000 0.2148 0.0000 0.2091 0.0000 0.1270 0.0000 0.1985 0.0000 0.1735 0.0000 0.1519 0.0000 0.2448 0.0000 0.0916 0.0000 0.7861 0.0000 0.2148 0.0000 0.1270 0.0000 0.1735 0.0000 0.2448 0.0000 0.7861 0.0000

Table 1: Estimation results for the MAACD model.

The obtained results allow for the following interpretation:

Table 1: Estimation resultscoefficients ( )model. the quite strong persistence of the ^k · High autoregressive for the MAACD prove

The obtained results allow for theespecially pronounced for submissions of the least duration process, which is following interpretation: aggressive limit orders. The highest coefficients correspond to the BQS the ^ · High autoregressive coefficients (k ) prove the quite strong persistence ofand BQB orders. We could risk saying pronounced for these orders are not as duration process, which is especiallyat this point thatsubmissions of the least much information-motivated as the market and inside-the-quotes orders and aggressive limit orders. The highest coefficients correspond to the BQS and that the decision to submit them is not so vulnerable to the flow of short-lived BQB orders. We could risk saying at this point that these orders are not as information that may quickly lose its value. Accordingly, the clustering of much information-motivated as the market and inside-the-quotes orders and behind-the-quote orders is most persistent, which means that the forecasted that the decision to submit them is not so vulnerable to the flow of short-lived duration has a longer memory with respect to the past history of order submisinformation that may quickly lose its value. Accordingly, the clustering of ^ sions. On the other hand, the smallest coefficients can be observed for orders behind-the-quote orders is most persistent, which means that the forecasted duration has a longer memory with respect to the past history of order submis17 ^ sions. On the other hand, the smallest coefficients can be observed for orders 17

20

N a t i o n a l

B a n k

o f

P o l a n d

The Empirical Application

that are placed inside of the best quotes, which means that they do not rely as much on the information from the distant past, especially in comparison to behind-the-quote orders. · The coefficients l,k represent "regime-switching" intercepts that change with ^ the type of the preceding order. A closer look at the various values of these estimates for the MS and MB durations (the first column in Table 1) allows for the following conclusion: the coefficient 1,1 = -0.0437, corresponding to ^ the previous MS order, is the smallest among all other l,1 estimates and thus ^ means that the expected duration to a market sell will be most considerably shortened in result of a market sell. Analogously, the same observation emerges for the bid side of the market. From the contents within first column of the lower panel of the Table 1 we see that the obtained coefficient 6,6 = -0.0040 ^ is the smallest among all other intercepts l,6 , for l = 1, 2, ..., 10. Therefore, ^ realization of a market/marketable buy order exerts the strongest influence on decreasing the time until another market/marketable buy order occurs. This observation agrees with Biais (1995) showing that market orders cluster together as traders split large orders into small parts in an effort to limit the undesired price impact of a huge transaction. Interestingly, for the expected duration at the end of which an IQS order is observed (second column of the table 1), 5,2 = -0.0784 is the smallest intercept. This coefficient refers to ^ a previous cancellation of an order at the best ask (best sell order). Quite naturally then, such an action results in a new submission of a best limit sell ^ order. The coefficient 6,2 = 0.1420 is the second smallest among l,2 , which ^ means that transactions at the ask (buys) also accelerate the submissions of best limit sell orders that establish the new most competitive ask price. This results from a price-reverting behavior, a kind of a micro cycle build from phases of liquidity consumption and replenishment as predicted by Parlour (1998) (see Hypothesis H1). Execution of a MB order exhausts liquidity on the ask side of a market and dealers can compete for an ask price that is at least one tick (pip) better than the current one. Analogously, a symmetrical pattern can be observed for the arrival rates of the IQB orders (the second column in lower panel of Table 1). The expected duration to posting an inside-the-quote buy shrinks most considerably after a cancellation on the same market side be^ cause 10,7 = -0.1800 is the smallest intercept among all other l,7 estimates. ^ The second smallest coefficient is 1,7 = 0.1547; this corresponds to a previous ^ market sell. As a general rule the expected waiting times to market/marketable and inside18 ^ ^ ^ ^ the-quotes order submissions intercepts 4,1 , 4,2 and 9,6 , 9,7 are quite large in value. This can mean that these most aggressive and price-improving orders are (at least to some extent) information-motivated and do not have the tendency to follow any behind-the-quote orders that are hidden in the depth of the order book. The MS and MB durations will also rise in value if a canWORKING PAPER No. 104 cellation occurs. Thus, if the bid-ask spread widens after a cancellation on any side of a market, the transaction costs of the MB or MS orders will be higher.

5

21

The Empirical Application

As a general rule the expected waiting times to market/marketable and inside^ ^ ^ the-quotes order submissions intercepts 4,1 , 4,2 and 9,6 , 9,7 are quite large ^ in value. This can mean that these most aggressive and price-improving orders are (at least to some extent) information-motivated and do not have the tendency to follow any behind-the-quote orders that are hidden in the depth of the order book. The MS and MB durations will also rise in value if a cancellation occurs. Thus, if the bid-ask spread widens after a cancellation on any side of a market, the transaction costs of the MB or MS orders will be higher. In this case it will be more profitable to place an inside-the-quote limit buy or sell order than a market order. The expected AQS duration shrinks most considerably in the presence of the ^ AQS order (^ 3,3 = 0.2432 is the smallest coefficient among l,3 ). For the bid side of the market 1,8 = 0.5206 is the smallest in value and thus the ex^ pected AQB duration shrinks most considerably in the presence of the MS order. Watching the dynamics of the market sell may enhance FX dealers to submit more orders at the best bid as the probability of their execution rises. The arrival rate of behind-the-quote orders is strongly linked to the arrival of market orders posted on the opposite side of the market. In terms of BQS orders, the smallest intercept, 6,4 = 0.1479, corresponds to the previous MB ^ order. Symmetrically, for the BQB orders, 1,9 = 0.0657 is the smallest in ^ value thus pointing to the former MS order. This confirms that limit orders are perceived by market participants as a kind of a bet on the level of the FX rate. Once there is a chance that the price will move upward as a result of a large buy trade (induced by a MB order), BQS orders become more profitable and so they increase significantly. At the same time if there is an opportunity for the price to move downward as a result of a market sell (induced by a MS order), traders bet on the scale of this movement and place the BQB orders more frequently. It is also possible that if traders anticipate a rise (a drop) in the FX rate they will post a MB (a MS) order and later a BQS (a BQB) order just to close their currency position and to realize their gains more quickly. A series of unexpected results were obtained for the best order cancellations. Interestingly, the expected time to sell (buy) best limit order cancellations shrinks most considerably after an AQS (AQB) order (^ 3,5 = -0.1009 is the ^ ^ smallest among l,5 and 8,10 = 0.0350 is the smallest among l,10 coefficients). ^ This means that many orders, once entered into an order book at the prevailing best quotes, are quickly withdrawn from the market before any other dealer can react. One explanation for this may be a type of "spoofing" practice. Traders 19 insert very short-lived "fleeting" orders and have no intention of executing a trade at the submitted price. Such actions are supposed to move the exchange rate down or up. Once an order appears and then subsequently disappears the illusion of excess demand or excess supply at the best quotes can influence the actions of other traders and move the rate in a desirable direction. · The l,k coefficients inform how the duration observed between two events that directly precede the current one urge or delay N a t i otrader actions. These oco-a future n a l B a n k o f P l efficients are responsible for a strong clustering of order durations. However, it should be mentioned, that the comparison of this impact among durations

5

22

n d

react. One explanation for this may be a type of "spoofing" practice. Traders insert very short-lived "fleeting" orders and have no intention of executing a The Empirical Application trade at the submitted price. Such actions are supposed to move the exchange rate down or up. Once an order appears and then subsequently disappears the illusion of excess demand or excess supply at the best quotes can influence the actions of other traders and move the rate in a desirable direction. · The l,k coefficients inform how the duration observed between two events that directly precede the current one urge or delay future trader actions. These coefficients are responsible for a strong clustering of order durations. However, it should be mentioned, that the comparison of this impact among durations attributed to different classes cannot be performed with the obtained coefficients values. Such a reasoning stems from the fact that the unconditional (with respect to Fi-1 ) expected durations that end up in particular states are also different in value. Some classes of durations (i.e the MB durations or the BQS durations) can be on average much shorter or much longer than the others. This means that we should not compare the coefficients l,k for a selected duration ending with a state yk . For example, if we look at l,1 estimates for the expected MS duration we see that they differ in value (for l = 1, 2, ..., 10). However, each of these coefficients relates to the realization of a different duration xi-1,l if the state yl was observed at the time t - 1 (see Equation 4). Because each of the durations xi-1,l (for l = 1, 2, ..., 10) has a different distribution that is characterized by its distinct conditional expectation i-1,l and shape parameter l , the corresponding coefficient values l,1 cannot be directly compared. We should not compare the coefficients values across the current state k (the coefficients in the same column of Table 1), although we could do this for the state l (the coefficients in the same row of Table 1). Looking at the parameter estimates presented in Tables (1), it is not possible to establish ad hoc the most probable sequence that describes when orders of a given type would most probably enter into the trading system. The difficulty arises from the considerable size of the model, a huge number of estimated coefficients and the construction of the model for the the outcome variable xi = min(xi,1 , xi,2 , ..., xi,10 ). The expected time until a particular state depends not only on the type of preceding order but also on the length of time prior to this order. Analytical formulas for the conditional (with respect to Fi-1 and not the current duration xi ) transition probabilities do not have a closed analytic form. Moreover, the comparison of conditional expectations 20 of durations that end up in selected states are not enough to make predictions about the future precedence of events. In our competing risk framework, ten competing durations xi,k that construct the process of a realized duration xi = min{x1,i , ..., x10,i } are characterized by different Weibull distributions. These distributions have not only different conditional expectations k,i but also different shape parameters k . The shape parameter has an impact on the concentration of the probability mass near zero. Therefore, the answer to the question of which duration, xi,k , wins the competition at time point ti by being the shortest depends on both factors: the conditional expected values of their distributions (hence i,k ) and the different skewness of these distributions (hence k ). In order to obtain the most probable chronological order according to which selected events occur, we can use an easy way of simulating data from the MAACD model. The simulation algorithm can be outlined as following:

WORKING PAPER No. 104

5

23

xi = min{x1,i , ..., x10,i } are characterized by different Weibull distributions. The These distributions have not only different conditional expectations Empirical Application k,i but also different shape parameters k . The shape parameter has an impact on the concentration of the probability mass near zero. Therefore, the answer to the question of which duration, xi,k , wins the competition at time point ti by being the shortest depends on both factors: the conditional expected values of their distributions (hence i,k ) and the different skewness of these distributions (hence k ). In order to obtain the most probable chronological order according to which selected events occur, we can use an easy way of simulating data from the MAACD model. The simulation algorithm can be outlined as following: ^ 1. For i = 1, set initial values for i,k as mean estimates of (observable) series xi,k (for k = 1, 2, ..., 10). 2. For k = 1, 2, ..., 10, draw n values of j,k (j = 1, 2, ..., n) from independent Weibull distributions. Each distribution is characterized by the corresponding shape parameter k . ^ ^ ^ ^ ^ 3. Compute xi,k = i,k i,k , where i,k = i,k · µ-1 = i,k ((1 + k -1 ))-1 . ^ k 4. Set yi = l and xi = xi,l if a duration xi,l is the shortest (for l = 1, 2, ..., 10), i.e. xi,l = min{xi,1 , ..., xi,l , ..., xi,10 }.

5

^ 5. Compute i+1,k with obtained yi and xi . 6. Iterate from (3) where i=i+1. With the application of the algorithm we can obtain one simulated series of artificial data generated from the MAACD model. With this simulated time series, we are able to compute marginal expectations for all latent durations, hence 1 ^ ^ E(xi,k ) = N N xi,k . These values could be treated as proper initial values for 1,k i=1 ^ in the first step of the second run of the simulation. We performed three runs of the simulations each time having sampled 1,000,000 realizations of the pair (xi , yi ). The accuracy of the last run of the performed simulation has been checked, because we reestimated the MAACD model with the simulated 21 data series and obtained estimates that were very similar to initial parameter values (with an accuracy equal to a second or third digit right of the decimal point).

24

The simulation output can be of importance if one wants to compute the frequencies that proxy the unconditional transition probabilities between the ten selected classes of orders. The simulation results are presented in Table (2). In the first column of the table we indicate the class of an order submitted or cancelled at time ti-1 (i.e. the type of the preceding order). The further ten columns correspond to obtained frequencies of events that took place at ti . For example, in the first row of Table (2), we show the estimate of the transition probability that after a MS order another MS order (column 2), IQS order (column 3), AQS order (column 4), BQS order (column 5), CS order (column 6), MB order (column 7), IQB order (column 8), AQB order (column 9), BQB order (column 10) or CB order (column 11) is observed. Thus, the elements in each row of the table must sum to one. The obtained results can be summarized as this:

N a t i o n a l B a n k o f

P o l a n d

· We confirm the Hypotheses 1. After the occurrence of a MS order an IQB order is the most likely (19.4 % cases). However, the following MS orders are

The Empirical Application

the table we indicate the class of an order submitted or cancelled at time ti-1 (i.e. the type of the preceding order). The further ten columns correspond to obtained frequencies of events that took place at ti . For example, in the first row of Table (2), we show the estimate of the transition probability that after a MS order another MS order (column 2), IQS order (column 3), AQS order (column 4), BQS order (column 5), CS order (column 6), MB order (column 7), IQB order (column 8), AQB order (column 9), BQB order (column 10) or CB order (column 11) is observed. Thus, the elements in each row of the table must sum to one. The obtained results can be summarized as this: · We confirm the Hypotheses 1. After the occurrence of a MS order an IQB order is the most likely (19.4 % cases). However, the following MS orders are nearly as frequent as the IBQ (18.5 % cases). Symmetrically, after a MB order an IQS order takes place 19.7 % of the time or another MB order 19.5 % of the time. As predicted by Parlour (1998), market sell (market buy) orders absorb liquidity from the market. As a result of that the bid-ask spread widens and it becomes more costly to cross the market and initiate an immediate trade. Thus, it is more profitable for traders who want to buy (sell) to use limit orders and to compete for the bid (ask) price that is at least one pip (tick) better than the current quote. The obtained regularity agrees with results of Lo & Sapp (2008), who document a kind of a book rebalancing scenario. Our result expand upon their findings since we differentiate between the sides of the market and prove that after a market sell (buy) the arrival of the best sell (buy) limit order is the most probable. On the other hand, we also document the follow-on strategy outlined by Biais (1995) which shows that market buy (sell) orders arrive in clusters. The events with the smallest probability are the AQB and AQS orders (about 4-5 % of cases); this is simply due to the small number of these orders in our data. We also confirm the Hypothesis 2 as the probability of observing a MS after a MB order or vice versa is very small (about 8 % of cases). This confirms the "crowding out" effect outlined by Parlour (1998).

· After the arrival of an IQS order the22 most frequent event is a MB order (about 14 % of cases). Symmetrically, after an IQB order a MS order is expected to arrive. Submission of the inside-the-quote order decreases the bid-ask spread and creates a kind of enhancement for the opposite side of the market to execute a profitable transaction. We also see that orders placed inside-thequotes tend to follow each other. This proves the "diagonal effect" that is demonstrated also in Goettler et al. (2005). Yeo (2002) predicts that if a new limit order changes the best price then the former best order will be cancelled and resubmitted at the new and better price. Hasbrouck & Saar (2009) report that this kind of "price-chasing" scenario is a possible explanation for existence of fleeting orders.

5

· As expected, AQS and AQB orders are most probably followed by CS and CB events (about 16 % of cases). This can be explained by the possible spoofing practice. AQS and AQB orders tend also to be followed by IQS and the IQB orders (about 13 % of cases), respectively. This finding relates closely to the depth of the order book and supports the Hypothesis 4. The submission of an at-the-quote order lengthens the queue of orders that wait for realization at WORKING PAPER No. 104 the best prices available. These dealers who want to buy or to sell would rather "jump-the-queue" and submit an inside-the-quote order to get the priority of execution (about 13 % of cases) or even submit a market order (about 11 %

25

that this kind of "price-chasing" scenario is a possible explanation for existence of fleeting orders.

The Empirical Application

· As expected, AQS and AQB orders are most probably followed by CS and CB events (about 16 % of cases). This can be explained by the possible spoofing practice. AQS and AQB orders tend also to be followed by IQS and the IQB orders (about 13 % of cases), respectively. This finding relates closely to the depth of the order book and supports the Hypothesis 4. The submission of an at-the-quote order lengthens the queue of orders that wait for realization at the best prices available. These dealers who want to buy or to sell would rather "jump-the-queue" and submit an inside-the-quote order to get the priority of execution (about 13 % of cases) or even submit a market order (about 11 % of cases). · BQS and BQB orders are unobservable thus traders cannot react to them directly. Nevertheless, their arrival rates reflect certain market conditions which can influence trader behavior indirectly. The most striking observation is their clustering effect. The placement of the BQS (BQB) order induces more BQS (BQB) orders, which means that the process of liquidity supply is characterized by clustering. · Cancellations of best orders tends to be followed by submission of the best inside-the-quote orders on the same market side. This observation is striking since about 28 % of events that succeed CS order are IQS orders and about 31 % of the events that follow CB orders are IQB orders. After a cancellation of the best order there will be a free space (of at least one unit) for another best order placed on the same market side.

5

MS IQS AQS BQS CS MB IQB AQB BQB CB

MS 0.185 (2) 0.110 (5) 0.111 (3) 0.103 (5) 0.104 (3) 0.080 (5) 0.137 (1) 0.103 (6) 0.134 (2) 0.062 (7)

IQS 0.131 (3) 0.122 (3) 0.133 (2) 0.130 (3) 0.281 (1) 0.197 (1) 0.136 (2) 0.113 (4) 0.131 (3) 0.134 (2)

AQS 0.043 (10) 0.065 (9) 0.079 (8) 0.063 (9) 0.061 (8) 0.055 (8) 0.046 (10) 0.050 (10) 0.054 (9) 0.042 (10)

BQS 0.077 (6) 0.112 (4) 0.107 (5) 0.158 (1) 0.093 (4) 0.114 (4) 0.100 (7) 0.094 (7) 0.099 (6) 0.089 (4)

CS 0.081 (5) 0.105 (6) 0.156 (1) 0.072 (8) 0.081 (6) 0.048 (9) 0.071 (8) 0.061 (9) 0.072 (7) 0.053 (8)

23

MB 0.075 (7) 0.142 (1) 0.111 (4) 0.139 (2) 0.067 (7) 0.195 (2) 0.114 (4) 0.118 (3) 0.109 (5) 0.095 (3)

IQB 0.194 (1) 0.126 (2) 0.106 (6) 0.122 (4) 0.131 (2) 0.127 (3) 0.120 (3) 0.133 (2) 0.130 (4) 0.312 (1)

AQB 0.046 (9) 0.040 (10) 0.038 (10) 0.041 (10) 0.035 (10) 0.037 (10) 0.058 (9) 0.065 (8) 0.048 (10) 0.051 (9)

BQB 0.114 (4) 0.103 (7) 0.094 (7) 0.098 (6) 0.087 (5) 0.074 (6) 0.106 (6) 0.105 (5) 0.158 (1) 0.089 (5)

CB 0.049 (8) 0.070 (8) 0.061 (9) 0.072 (7) 0.059 (9) 0.073 (7) 0.113 (5) 0.157 (1) 0.065 (8) 0.074 (6)

Table 2: Transition probabilities ­ simulation results. Column (1) contains a type of a directly preceding event. Numbers in brackets sort the transition probabilities in a descending order.

6

Impact of the Explanatory Variables

In order to examine potential microstructure factors that may have an impact on order choice and the pace of order submissions/cancellations, we enriched the MAACD model with the following explanatory variables: · Bid-ask spread (spr ), defined as the difference between the best ask price and the best bid price in the system before the moment of order submission/cancellation. · Ask depth (adep) and bid depth (bdep), defined as the cumulated sizes of limit orders offered to sell (buy) at the best ask and at the best bid price, respectively.

26

· Ask depth and bid depth dummies (adepd, bdepd ). o Thel indicators oare P o l a equal N a t i n a B a n k f to one if the ask depth or the bid depth is larger than 10 M. EUR and if the actual amount of depth is hidden.

n d

IQB 0.137 (1) 0.136 AQB 0.103 (6) 0.113 BQB 0.134 (2) 0.131 Impact of the Explanatory(7) Variables CB 0.062 0.134

(2) (4) (3) (2)

0.046 (10) 0.050 (10) 0.054 (9) 0.042 (10)

0.100 0.094 0.099 0.089

(7) (7) (6) (4)

0.071 0.061 0.072 0.053

(8) (9) (7) (8)

0.114 0.118 0.109 0.095

(4) (3) (5) (3)

0.120 0.133 0.130 0.312

(3) (2) (4) (1)

0.058 (9) 0.065 (8) 0.048 (10) 0.051 (9)

0.106 0.105 0.158 0.089

(6) (5) (1) (5)

0.113 0.157 0.065 0.074

(5) (1) (8) (6)

Table 2: Transition probabilities ­ simulation results. Column (1) contains a type of a directly preceding event. Numbers in brackets sort the transition probabilities in a descending order.

6

Impact of the Explanatory Variables

In order to examine potential microstructure factors that may have an impact on order choice and the pace of order submissions/cancellations, we enriched the MAACD model with the following explanatory variables: · Bid-ask spread (spr ), defined as the difference between the best ask price and the best bid price in the system before the moment of order submission/cancellation. · Ask depth (adep) and bid depth (bdep), defined as the cumulated sizes of limit orders offered to sell (buy) at the best ask and at the best bid price, respectively. · Ask depth and bid depth dummies (adepd, bdepd ). The indicators are equal to one if the ask depth or the bid depth is larger than 10 M. EUR and if the actual amount of depth is hidden. · Ask and bid quote slopes (askQS, bidQS ). Ask quote slope is defined as the ratio of the difference between the worst (the highest) ask price prevailing in worst best the system (Pask ) and the best ask price (Pask ) to the cumulated (whole) m ask depth ( i=1 Sizeask,i ): askQS =

worst best Pask - Pask m i=1 Sizeask,i

(8)

6

Bid quote slope is defined as the ratio of the difference between the best bid best price (Pbid ) and the worst (the lowest) bid price prevailing in the system worst (Pbid ) to the cumulated (whole) bid depth ( n Sizebid,i ): i=1 bidQS =

best worst Pbid - Pbid n i=1 Sizebid,i

(9)

· EUR/PLN rate volatility (vol ), constructed as a realized volatility estimate 24 for the past 10 minutes prior to the moment of order submission. In order to calculate realized volatility estimate, log returns of all observable mid prices have been used. · EUR/PLN return (ret), as the log return of the EUR/PLN mid price during past 10 minutes prior to the moment of a given event. · EUR/USD return (EURUSDret), as the log return of the EUR/USD mid price during past 10 minutes prior to the moment of a given event. · Two time-of-day dummies that describe possible fluctuations in the disproportion of selected order types: (1) the morning effect (begin) (d1 dummy is equal to 1 if an order is submitted between 8:00 and 8:30 and is equal to zero otherwise), (2) the afternoon effect (end ) (d2 dummy is equal to 1 if an order is placed between 17:30 and 18:00 and is equal to zero otherwise).

WORKING PAPER No. 104

These explanatory variables that were characterized by a cyclical behaviors (the bidask spread, the ask and bid quote slopes, the realized volatility estimate) have been

27

· EUR/USD return (EURUSDret), as the log return of the EUR/USD mid price Impact of the Explanatory Variables during past 10 minutes prior to the moment of a given event. · Two time-of-day dummies that describe possible fluctuations in the disproportion of selected order types: (1) the morning effect (begin) (d1 dummy is equal to 1 if an order is submitted between 8:00 and 8:30 and is equal to zero otherwise), (2) the afternoon effect (end ) (d2 dummy is equal to 1 if an order is placed between 17:30 and 18:00 and is equal to zero otherwise). These explanatory variables that were characterized by a cyclical behaviors (the bidask spread, the ask and bid quote slopes, the realized volatility estimate) have been initially deseasonalized. Diurnality factors were estimated with a formula (7). After such a transformation the series depicts a kind of "innovation" that is independent from the repetitive day-by-day seasonal pattern.

6

Figure 3: Diurnality pattern for the bid-ask spread, the realized volatility, the bid quote slope and the ask quote slope.

25 The estimation results are presented in Table 4. Interestingly, after the inclusion of the explanatory variables in the MAACD specification the parameters responsible for the persistence of MB and MS order submissions changed. Parameter estimates ^ ^ for the market order durations, 1 = 0.3976 and 6 = 0.4475, are much smaller than in the initial specification without explanatory variables. This means that the additional factors took over much of the duration variation. It further confirms our hypothesis that in the event of the most aggressive orders, very prompt information flows reflected by changes in market microstructure features (i.e. the bid-ask spread, depth, volatility, past returns) are the major driving force behind the pace of their submissions. As the persistence of the process decreased the impact of the information from the distant past has a smaller value. In the next chapter we will present the impact of the individual factors.

6.1

28

Bid-Ask Spread

As suggested by the theoretical literature (Foucault (1999)), we document the significant negative impact11 (at a 1 % significance level)o of a l bid-ask spread oon athed N a t i n the B a n k o f P l n expected time to a MB or a MS order. Thus, the increase in the bid-ask spread deflates the probability of market/marketable order submissions. Simultaneously, it

Impact of the Explanatory Variables

flows reflected by changes in market microstructure features (i.e. the bid-ask spread, depth, volatility, past returns) are the major driving force behind the pace of their submissions. As the persistence of the process decreased the impact of the information from the distant past has a smaller value. In the next chapter we will present the impact of the individual factors.

6.1

Bid-Ask Spread

As suggested by the theoretical literature (Foucault (1999)), we document the significant negative impact11 (at a 1 % significance level) of the bid-ask spread on the The estimation results are presented in Table 4. Interestingly, after the inclusion of expected time to a MB or a MS order. Thus, the increase in the bid-ask spread the explanatory variables in the MAACD specification the parameters responsible deflates the probability of market/marketable order submissions. Simultaneously, it for the persistence of MB and MS order submissions changed. Parameter estimates significantly increases the probability that an IQB or ^ IQS order is placed in the sys^ for the market order durations, 1 = 0.3976 and 6 = 0.4475, are much smaller tem. This finding is consistent with the results of a number of empirical studies (i.e. than in the initial specification without explanatory variables. This means that the Biais (1995); Harris (1998); Bae et al. (2003); Ranaldo (2004); Ellul et al. (2007)). additional factors took over much of the duration variation. It further confirms our Hitting or taking the quotes is much more expensive if the bid-ask spread is large hypothesis that in the event of the most aggressive orders, very prompt information and traders prefer to consume liquidity when it is cheap. On the other hand, it is flows reflected by changes in market microstructure features (i.e. the bid-ask spread, much more profitable for market participants to provide liquidity in the form of IQB depth, volatility, past returns) are the major driving force behind the pace of their ^ ^ or IQS limit orders. As the coefficients spr,2 and spr,7 are significant and negative, submissions. As the persistence of the process decreased the impact of the informathe wide bid-ask spread encourages the submission of the most competitive limit tion from the distant past has a smaller value. In the next chapter we will present orders. If the bid-ask spread is wide it is easier to compete for the price that is at the impact of the individual factors. least one tick (pip) better then the current one, as it would improve the likelihood of an order execution at a very small expense. Hence, we confirm the Hypothesis 6.1 Bid-Ask Spread 4. The rise in the bid-ask spread also prompts the submission of at-the-quotes and As suggested by orders on both sides of (Foucault (1999)), we document the sigbehind-the-quotes the theoretical literature the market. A possible explanation for nificant negative impact11 (at a 1 % significance level) of the bid-ask spread on the this is that when the bid-ask spread rises as a result of an adverse selection risk the expected time place orders that order. Thus, the increase in the bid-ask avoid traders prefer toto a MB or a MSare far away from the midquote in order to spread deflates the probability of market/marketable order submissions. Simultaneously, it 11the risk of being "picked-off". Although the coefficients corresponding to the bidIn the sample there are 92,818 observations. We rest on the assumption that the number of significantly increases the base our inference on IQB or IQS normality of the maximum ask spread in largecase of at-the-quote and behind-the-quoteorder is are negative and observations is the enough to probability that an the asymptotic orders placed in the sys2 ^ tem. This finding likelihood estimator ^ consistent level), they are of been estimated as: A = N compared significant (at a 5 issignificance with theand B have a number of empirical1studiesLnLi % N (, A-1 BA-1 ). A results very small in value when N (i.e. i N LnLi LnLi 1 ^ BBiais i (or Harris (1998); orders. Accordingly, the (2004); Ellul has (2007)). to = N (1995);inside-the-quote Bae et al. (2003); Ranaldobid-ask spreadet al. a much market ) ( ). Hitting or taking the quotes is of the most aggressive the bid-ask impact of the greater impact on the arrival ratemuch more expensive if orders. The spread is large 26 and traders prefer to consume liquidity when it is cheap. On the although slight bid-ask spread is rather symmetric on the ask and bid market side other hand, it is much more profitable for market participants to provide a MS order (i.e. sell EUR disproportions can be observed. The expected duration toliquidity in the form of IQB ^ or IQS limit reacts As the coefficients ^spr,2 and the bid-ask spread than the exand buy PLN) orders. more strongly to theincrease ofspr,7 are significant and negative, the wide bid-ask to a MB order (buy EUR and sell PLN). Maybe this is because pected waiting timespread encourages the submission of the most competitive limit a orders. Ifof the bid-ask spread could be is easier to compete for and price that isin fraction the bid-ask spread is wide it information-motivated the an increase at least one selection costs then in current one, as it would improve the likelihood the adversetick (pip) betterresultsthe a different valuation of the open currency poof an order execution at a Polish zloty. Investments in zloty are treated as more sitions in euros versus in the very small expense. Hence, we confirm the Hypothesis 4. The so in probability of aggressive selling the submission of at-the-quotes and risky andrise the the bid-ask spread also promptsdeflates in a more considerable way. behind-the-quotes the increase in the of the spread A possible explanation for We also report that orders on both sidesbid-ask market. induces more cancellations ^ this is that when the bid-ask coefficients as a and ^of an adverse selection a 5 % on the both market sides. The spread rises spr,5resultspr,10 are significant (atrisk the traders prefer to place orders that when away from the midquote in order to avoid level) and negative but quite small are farcompared with the impact of the bid-ask

11

6

spread on the MS orare 92,818 observations. We rest cannot assumption that the number of In the sample there MB durations. Therefore, we on the support the hypothesis H6 that small bid-ask spread inducesour inference on the asymptotic normalityorders maximum observations is large enough to base more cancellations while best limit of the tend to N 2 LnL 1 ^ ^ likelihood estimator N by -1 BA-1 orders. On the contrary, if as: bid-ask spread i be cancelled and replaced(, Amarket ). A and B have been estimated the A = N i N 1 ^ B = N i ( LnLi ) ( LnLi ). widens, traders tend cancel the best orders and replace them by more competitive to ones. 26

WORKING PAPER No. 104

6.2

Depth

29

The second important microstructure variables are the ask and the bid depths. An

a fraction of the bid-ask spread could be information-motivated and an increase in Impact the Explanatory pothe adverse selection costs results in a different valuation of the openofcurrency Variables sitions in euros versus in the Polish zloty. Investments in zloty are treated as more risky and so the probability of aggressive selling deflates in a more considerable way. We also report that the increase in the bid-ask spread induces more cancellations ^ ^ on the both market sides. The coefficients spr,5 and spr,10 are significant (at a 5 % level) and negative but quite small when compared with the impact of the bid-ask spread on the MS or MB durations. Therefore, we cannot support the hypothesis H6 that small bid-ask spread induces more cancellations while best limit orders tend to be cancelled and replaced by market orders. On the contrary, if the bid-ask spread widens, traders tend to cancel the best orders and replace them by more competitive ones.

6.2

Depth

6

The second important microstructure variables are the ask and the bid depths. An increase in the size of orders that are offered at the best prices on both sides of the market inflates the probability that a MS order will arrive as predicted by the ^ ^ hypothesis H3. The negative coefficients adep,1 and bdep,1 prove that a rise in these observable liquidity measures shortens MS durations. A large depth at the best bid encourages aggressive sells. Therefore, if a trader wants to execute a high-volume sell order, sufficient depth at the best bid guarantees a prompt execution without the risk of hitting an unfavorable price. This "enhancement effect" is additionally ^ pronounced by the significant (at a 1 % level) coefficient bdepd,1 = -0.4484, indicating that a depth of more than 10 M. EUR is hidden at the best bid. Such a signal could be interpreted as additional encouragement for submitting aggressive sell orders. On the other hand, we obtained a negative and significant (at a 1 % ^ level) coefficient adep,1 = -0.048 thus the increase in the size of best limit sell orders prevailing in the system induces more sell trades. The large depth at the best ask can have an informative meaning for the context of a quasi-technical analysis performed 27 by market participants (see Osler (2003); Ellul et al. (2007)). An increase in the ask depth may indicate a near future drop in the exchange rate. Ellul et al. (2007) found a similar result for the NYSE stocks and called it the "short-term forecasting hypothesis". Similar results as for MS durations can be found for MB durations. An increase in the market depth, either at the best ask or at the best bid, exerts a significant positive influence on the probability of submitting an aggressive market order. Although, the corresponding depth dummies are insignificant. Thus, the results support the hypothesis H3. It is interesting to note that in the case of MB durations the impact of the ask depth is slightly larger than the impact of the bid depth as we have ^ ^ |adep,6 | > |bdep,6 |. Analogously, for MS orders the following equation holds true ^ ^ |adep,1 | < |bdep,1 |. The inequalities evidence that the "enhancement effect" is more pronounced than the effect of the "short-term forecasting effect" of Ellul et al. (2007). As far as IQB and IQS orders are concerned, we find perfect evidence for the "jump the queue" hypothesis as stated in Ellul et al. (2007). The large depth at the best ask prompts the submission of best limit sell orders that improve on the current price ^ (adep,2 < 0). Accordingly, the large depth at the best bid encourages traders to post a limit buy order with a price at least one tick better in order to gain execution N a t i o n P o l a n ^ ^ an B a n k o priority (bdep,7 < 0 and bdepd,7 < 0). On the other hand, a l increase in fthe visible d depth on the bid (ask) side hinders the pace of the IQS (IQB) orders as forecasted by the "short-term forecasting hypothesis".

30

pact of the ask depth is slightly larger than the impact of the bid depth as we have ^ ^ |adep,6 | > |bdep,6 |. Analogously, for MS orders the following equation holds true Impact of the Explanatory Variables ^ ^ |adep,1 | < |bdep,1 |. The inequalities evidence that the "enhancement effect" is more pronounced than the effect of the "short-term forecasting effect" of Ellul et al. (2007). As far as IQB and IQS orders are concerned, we find perfect evidence for the "jump the queue" hypothesis as stated in Ellul et al. (2007). The large depth at the best ask prompts the submission of best limit sell orders that improve on the current price ^ (adep,2 < 0). Accordingly, the large depth at the best bid encourages traders to post a limit buy order with a price at least one tick better in order to gain execution ^ ^ priority (bdep,7 < 0 and bdepd,7 < 0). On the other hand, an increase in the visible depth on the bid (ask) side hinders the pace of the IQS (IQB) orders as forecasted by the "short-term forecasting hypothesis". The impact of depth on AQS and AQB durations is significantly negative so that the large queue at the best quotes does not discourage traders to offer/bid more quantities at these prices. Such a result is difficult to explain. The submission of AQB and AQS orders rules out the priority of execution; nevertheless, at-the-quote orders have a tendency to arrive in clusters. The reaction of BQS and BQB orders to the changes in depth is much smaller in value but also lead to some interesting conclusions. The BQS durations shrink as a result of an increase in the depth at the best bid but lengthen with the depth at the best ask. Symmetric observation refers to BQB orders. The BQB duration shrinks as a result of an increase in the depth of the best ask. In agreement with the "short-term forecasting hypothesis", the increase in quantity offered to sell at the best ask signals a short-term price drop. Consequently, it increases the probability that a BQB order will be executed. Similarly, if there is a large order placed at the best bid, traders anticipate that the EUR/PLN rate will rise and thus a28 BQS order will be executed with greater probability. Conversely, large depth at the best ask deflates the probability of BQS order execution.

6

6.3

Quote Slopes

Quote slopes are totally unobservable for market participants and thus they cannot be taken into consideration when determining their order decisions. On the other hand, fluctuations in overall liquidity reflected in quote slopes may influence trader behavior indirectly. Periodic liquidity shocks with respect to bid or ask sides of the market induce certain trading choices. We observe that the quote slope of the ask side of the order book has a significant and positive impact on the expected IQS and AQS durations. An increase in the slope indicates a deterioration of the liquidity supply. If there is a liquidity squeeze on the ask side of an order book, the placement of the IQS and AQS orders slows down. The state of the order book is also closely bound to the value of the technical analysis. A lesser liquidity on the ask side signals an upward price pressure and thus traders restrain from submitting aggressive limit orders to avoid the risk of being picked off. Instead, traders submit more market ^ buy orders as can be observed from the significant negative coefficient askQS,6 . The steeper slope on the bid side of the market is correlated with the accelerated submission of MS, IQS and AQS orders. This can also be predicted from the "shortterm forecasting hypothesis" and can be explained by the fact that the state of the order book can be partially anticipated by traders on the basis of orders left by WORKING PAPER No. 104 their non-bank clients. Interestingly, the deterioration of the liquidity supply on the bid side of the market is linked with accelerated submission of MB and IQB orders, hence an increase in the overall trading activity.

31

bound to the value of the technical analysis. A lesser liquidity on the ask side signals an upward price pressure and thus traders restrain from submitting aggressive limit Impact of the Explanatory Variables orders to avoid the risk of being picked off. Instead, traders submit more market ^ buy orders as can be observed from the significant negative coefficient askQS,6 . The steeper slope on the bid side of the market is correlated with the accelerated submission of MS, IQS and AQS orders. This can also be predicted from the "shortterm forecasting hypothesis" and can be explained by the fact that the state of the order book can be partially anticipated by traders on the basis of orders left by their non-bank clients. Interestingly, the deterioration of the liquidity supply on the bid side of the market is linked with accelerated submission of MB and IQB orders, hence an increase in the overall trading activity.

MS, k=1 estimate p - value 0.5120 0.0000 1.4404 0.0000 1.5189 0.0000 1.9256 0.0000 1.0452 0.0000 1.8821 0.0000 0.9158 0.0000 1.9606 0.0000 1.6969 0.0000 2.3439 0.0000 0.3976 0.0000 0.2193 0.0000 0.1739 0.0000 0.2065 0.0000 0.2279 0.0000 0.3252 0.0000 0.3377 0.0000 0.2558 0.0000 0.3006 0.0000 0.3887 0.0000 0.3604 0.0000 0.7360 0.0000 1.2086 0.0000 -0.0480 0.0000 -0.0329 0.0000 0.2272 0.0859 -0.4484 0.0016 0.0217 0.1074 -0.1136 0.0000 -0.2640 0.0000 0.0061 0.0000 -0.0005 0.7596 0.0044 0.9444 0.1604 0.0086 ASK SIDE OF THE MARKET (SELL ORDERS) IQS, k=2 AQS, k=3 BQS, k=4 estimate p - value estimate p - value estimate p - value 0.9070 0.0000 0.6950 0.0000 0.5686 0.0000 1.6483 0.0000 0.5352 0.0000 0.4882 0.0000 1.2003 0.0000 0.3803 0.0000 0.6025 0.0000 1.4814 0.0000 0.8493 0.0000 0.3198 0.0000 0.2923 0.0000 0.6849 0.0000 0.5752 0.0000 0.3869 0.0000 0.5006 0.0000 0.1816 0.0000 1.4603 0.0000 0.9434 0.0000 0.5402 0.0000 1.5049 0.0000 0.8947 0.0000 0.5451 0.0000 1.4421 0.0000 0.9573 0.0000 0.6806 0.0000 1.3623 0.0000 1.0425 0.0000 0.6832 0.0000 0.6523 0.0000 0.8441 0.0000 0.8686 0.0000 0.1191 0.0000 0.1132 0.0000 0.1026 0.0000 0.1770 0.0000 0.1240 0.0000 0.1537 0.0000 0.2083 0.0000 0.1486 0.0000 0.1772 0.0000 0.2387 0.0000 0.1874 0.0000 0.1457 0.0000 0.1690 0.0000 0.1331 0.0000 0.0796 0.0000 0.0697 0.0000 0.0884 0.0000 0.0364 0.0017 0.2329 0.0000 0.1441 0.0000 0.1123 0.0000 0.2602 0.0000 0.1344 0.0000 0.0971 0.0000 0.2438 0.0000 0.1738 0.0000 0.1253 0.0000 0.2565 0.0000 0.1970 0.0000 0.1573 0.0000 0.8012 0.0000 0.7941 0.0000 0.7902 0.0000 -0.2029 0.0000 -0.0219 0.0024 -0.0161 0.0018 -0.0230 0.0000 -0.0088 0.0200 0.0047 0.0665 0.0104 0.0069 -0.0104 0.0005 -0.0088 0.0000 0.0361 0.6052 0.1380 0.0712 0.0642 0.2625 0.0275 0.7962 0.0430 0.6148 0.0473 0.4115 0.0141 0.0585 0.0131 0.0097 -0.0082 0.0065 -0.0132 0.0300 -0.0106 0.0191 0.0033 0.2596 -0.0029 0.7819 0.0059 0.4540 0.0070 0.1592 -0.0021 0.0004 -0.0017 0.0007 -0.0013 0.0005 -0.0001 0.9083 0.0014 0.0077 -0.0004 0.2760 0.0541 0.1007 0.0471 0.0698 0.0609 0.0004 -0.0679 0.0085 0.1835 0.0000 0.0666 0.0000 CS, k=5 estimate p - value 0.5411 0.0000 0.5061 0.0000 -0.0612 0.3029 1.0612 0.0000 1.0402 0.0000 1.1055 0.0000 1.0317 0.0000 1.0942 0.0000 1.1762 0.0000 1.1176 0.0000 0.7715 0.0000 0.1057 0.0000 0.1701 0.0000 0.1366 0.0000 0.1620 0.0000 0.2112 0.0000 0.1042 0.0000 0.1512 0.0000 0.1707 0.0000 0.2045 0.0000 0.1137 0.0000 0.7963 0.0000 -0.0317 0.0064 -0.0046 0.2758 0.0036 0.3294 -0.1506 0.0289 0.0323 0.7571 0.0016 0.7880 -0.0013 0.7938 0.0147 0.1107 0.0018 0.0018 0.0007 0.2283 0.0369 0.1781 0.0121 0.6100

6

parameters 1,k MS 2,k IQS 3,k AQS 4,k BQS 5,k CS 6,k MB 7,k IQB 8,k AQB 9,k BQB 10,k CB k 1,k MS 2,k IQS 3,k AQS 4,k BQS 5,k CS 6,k MB 7,k IQB 8,k AQB 9,k BQB 10,k CB k spr,k adep,k bdep,k adepd,k bdepd,k askQS,k bidQS,k vol,k ret,k EU RU SDret,k begin,k end,k

29

parameters 1,k MS 2,k IQS 3,k AQS 4,k BQS 5,k CS 6,k MB 7,k IQB 8,k AQB 9,k BQB 10,k CB k 1,k MS 2,k IQS 3,k AQS 4,k BQS 5,k CS 6,k MB 7,k IQB 8,k AQB 9,k BQB 10,k CB k spr,k adep,k bdep,k adepd,k bdepd,k askQS,k bidQS,k vol,k ret,k EU RU SDret,k begin,k end,k

MB, k=6 estimate p - value 1.8377 0.0000 0.6959 0.0000 1.6917 0.0000 1.4718 0.0000 2.0186 0.0000 0.3217 0.0000 1.1890 0.0000 1.3654 0.0000 1.8564 0.0000 1.1032 0.0000 0.4475 0.0000 0.3136 0.0000 0.2359 0.0000 0.3633 0.0000 0.3326 0.0000 0.3517 0.0000 0.2049 0.0000 0.1250 0.0000 0.2076 0.0000 0.3402 0.0000 0.3335 0.0000 0.7324 0.0000 1.1108 0.0000 -0.0489 0.0000 -0.0349 0.0000 0.0551 0.6419 0.0029 0.9852 -0.0249 0.0377 -0.0419 0.0003 -0.1693 0.0000 -0.0139 0.0000 0.0072 0.0000 0.2118 0.0009 0.0550 0.2649

BID SIDE OF THE MARKET (BUY ORDERS) IQB, k=7 AQB, k=8 BQB, k=9 estimate p - value estimate p - value estimate p - value 0.4381 0.0000 0.6530 0.0000 0.1089 0.0026 1.6300 0.0000 1.1895 0.0000 0.4382 0.0000 1.5650 0.0000 1.0634 0.0000 0.4908 0.0000 1.6438 0.0000 1.2553 0.0000 0.5919 0.0000 1.4878 0.0000 1.3046 0.0000 0.6718 0.0000 1.0124 0.0000 0.9868 0.0000 0.5735 0.0000 1.8083 0.0000 0.7642 0.0000 0.4357 0.0000 1.4361 0.0000 0.7222 0.0000 0.5415 0.0000 1.6380 0.0000 1.1848 0.0000 0.2807 0.0000 0.1960 0.0001 0.9632 0.0000 0.4874 0.0000 0.6181 0.0000 0.7909 0.0000 0.8824 0.0000 0.0539 0.0000 0.0439 0.0241 0.0295 0.0040 0.2218 0.0000 0.1771 0.0000 0.0995 0.0000 0.2383 0.0000 0.1495 0.0000 0.1039 0.0000 0.2548 0.0000 0.1811 0.0000 0.1012 0.0000 0.2410 0.0000 0.1745 0.0000 0.1511 0.0000 0.1274 0.0000 0.1216 0.0000 0.1151 0.0000 0.1493 0.0000 0.1537 0.0000 0.1024 0.0000 0.2365 0.0000 0.1831 0.0000 0.1726 0.0000 0.2716 0.0000 0.2079 0.0000 0.1271 0.0000 0.1803 0.0000 0.2014 0.0000 0.0554 0.0008 0.7839 0.0000 0.7855 0.0000 0.7970 0.0000 -0.2401 0.0000 -0.0112 0.3121 -0.0143 0.0022 0.0105 0.0293 -0.0137 0.0060 -0.0109 0.0000 -0.0229 0.0000 -0.0112 0.0146 0.0024 0.2276 -0.0250 0.7924 0.1125 0.2491 0.0837 0.0490 -0.2029 0.0141 0.0290 0.7940 0.0254 0.6555 0.0175 0.0423 -0.0096 0.1614 0.0116 0.0003 -0.0203 0.0021 -0.0038 0.5423 -0.0094 0.0009 0.0276 0.0191 -0.0007 0.9516 0.0058 0.2113 0.0022 0.0014 0.0022 0.0028 0.0009 0.0041 -0.0004 0.6406 0.0007 0.3593 -0.0005 0.1159 -0.0492 0.1118 0.0337 0.2909 0.0294 0.0270 -0.0408 0.1660 0.1854 0.0001 0.0638 0.0000

CB, k=10 estimate p - value 1.2560 0.0000 1.2476 0.0000 1.3391 0.0000 1.3905 0.0000 1.3524 0.0000 0.8154 0.0000 0.6647 0.0000 0.1565 0.1066 1.3916 0.0000 1.4084 0.0000 0.7170 0.0000 0.1128 0.0000 0.1961 0.0000 0.2218 0.0000 0.2155 0.0000 0.1753 0.0000 0.1020 0.0000 0.2324 0.0000 0.1406 0.0000 0.1916 0.0000 0.2590 0.0000 0.7875 0.0000 -0.0450 0.0195 -0.0034 0.5070 -0.0080 0.0754 -0.1036 0.2198 -0.0228 0.8348 -0.0109 0.1011 0.0140 0.0469 0.0194 0.1183 -0.0026 0.0007 -0.0004 0.6584 0.0947 0.0069 0.0006 0.9819

Table 3: Estimation results for the MAACD model with explanatory variables.

30

32

N a t i o n a l B a n k o f P o l a n d

Impact of the Explanatory Variables

6.4

Volatility

We find a significant impact of the return volatility on the submissions of market orders (for both sides of the market) and inside-the-quotes limit orders (only for the bid side of the market). The impact is negative for MS and MB durations and positive for the IQB durations, contrary to predictions of Foucault (1999). Our results also do not confirm the findings of Lo & Sapp (2008) who report an overall trading decline in the presence of increased volatility. Thus, we do not find a support for the Hypothesis 5. The FX rate volatility is a traditional measure of market uncertainty. An increase in volatility increases the risk of being picked off and so the frequency of submitting best limit orders decreases. Handa & Schwartz (1996) report on the rationale of placing limit orders for informed or liquidity traders; they find that if volatility increases due to informed trading, the risk of being bagged by informed traders rises. This finding generally agrees with results of Fong & Liu (2010) who report that if traders observe a large price swing they will withdraw or relocate their orders away from the market price. On the other hand, in volatile periods traders close their currency positions that may be associated with the more intense use of ^ ^ market orders. Interestingly enough, we obtained the relation vol,1 < vol,6 , which means that traders accelerate buy transactions more considerably if they want to buy zloty (sell euro) than if they want to sell zloty (buy euro). As far as orders cancellations are concerned, volatility does not seem to significantly influence their arrival rate and thus we cannot support Hypothesis 7.

6

6.5

Momentum

Our results clearly confirm that the direction of the FX rate in the past 10 minutes has a significant impact on the order choice. Upward movement of the EUR/PLN rate, hence a Polish zloty depreciation, hinders placement of MS orders (market orders to sell euro and buy zloty) and enhances MB orders (market orders to buy euro and sell zloty). This means that traders act according to a momentum, or a trend-following strategy. The acceleration of MB order submissions is particularly ^ pronounced since the ret,6 is quite large in value. The selling pressure of the zloty makes IQB, AQB and BQB orders unprofitable since once the trend continues their ^ ^ ^ probability of execution declines (ret,7 > 0, ret,8 > 0, ret,9 > 0). Similarly, those traders who want to sell would rather use AQS or even BQB orders as there is a chance that they will be matched when the FX rate reaches a certain level. A zloty depreciation hinders cancellation of best limit sell orders whereas it prompts cancellation of best limit buys as predicted by a trend-chasing practice. We also observe a significant impact concerning EUR/USD changes on the submis31 sion rate of MB orders. If during the past 10 minutes the EUR/USD rate moves in the upward direction (dollar depreciates towards euro), the submission of market orders to buy euro and sell zloty will be deterred. In the period under study, the dollar depreciation was closely linked to a decrease in the global risk aversion and an increased interest in currencies of emerging markets. Therefore, traders refrained WORKING PAPER No. 104 from selling Polish zloty.

33

Impact of the Explanatory Variables

We also observe a significant impact concerning EUR/USD changes on the submission rate of MB orders. If during the past 10 minutes the EUR/USD rate moves in the upward direction (dollar depreciates towards euro), the submission of market orders to buy euro and sell zloty will be deterred. In the period under study, the dollar depreciation was closely linked to a decrease in the global risk aversion and an increased interest in currencies of emerging markets. Therefore, traders refrained from selling Polish zloty.

6.6

Time of day

The begin-of-day dummy is significantly positive and large in value for market orders to buy euro and sell Polish zloty. The coefficient is also positive for BQS and BQB (at the 5 % significance level) durations. This means that once trading begins, the provision of liquidity is deteriorated in comparison to the rest of the day. The submission of behind-the-quotes orders becomes unprofitable because of their small execution probability due to a slow trading intensity. The impact of the afternoon effect is quite similar; submissions of AQS, BQS, AQB and BQB orders are also less frequent. Additionally, traders refrain from aggressive buying of euro (selling zloty) in the morning and from aggressive selling of euro (buying zloty) at the end of the day. We were not able to confirm the conviction that market orders dominate trading in the beginning of a day whereas limit orders cluster at the end of a day (see Bloomfeld et al. (2005)).

6

6.7

Symmetry Restrictions

As the last step of our empirical analysis we tested some symmetry restrictions with respect to the impact of selected explanatory variables on order dynamics on an ask and bid side of a market. With a help of the likelihood ratio test we verified several null hypotheses about the equal impact of: 1.) the bid-ask spread, 2.) market depth, 3.) volatility and 4.) the bid/ask quote slopes on the pace of order submissions when traders intend to buy zloty (sell euro) versus when they intend to sell zloty (buy euro). Interestingly, in case of nearly all order submissions, the null of equal impact of selected microstructure factors should be rejected (at a 95 % confidence level). Only in case of order cancellations, the impact of all selected explanatory variables can be treated as equal for both market sides. Especially for market orders, the significant disproportions in coefficient values for the bid-ask spread, depth dummies, volatility and the quote slopes can be observed. The parameter estimates for the ask side 32 a market are much larger in value, which of means that the immediate decisions to buy zloty (sell euro) are significantly more sensitive to liquidity or information motivated factors. From this viewpoint, our general and richly parameterized duration model can be fully justified.

H0 : p - val : H0 : spr,1 = spr,6 0.0031 adep,1 = bdep,6 adepd,1 = bdepd,6 bdep,1 = adep,6 bdepd,1 = adepd,6 0.0012 vol,1 = vol,6 0.0000 askQS,1 = bidQS,6 bidQS,1 = askQS,6 0.0000 spr,2 = spr,7 0.0001 adep,2 = bdep,7 adepd,2 = bdepd,7 bdep,2 = adep,7 bdepd,2 = adepd,7 0.1150 vol,2 = vol,7 0.0064 askQS,2 = bidQS,7 bidQS,2 = askQS,7 0.0060 spr,3 = spr,8 0.0108 adep,3 = bdep,8 adepd,3 = bdep,8 bdep,3 = adep,8 bdepd,3 = adep,8 0.0794 vol,3 = vol,8 0.0108 N a askQS,3 = bidQS,8 bidQS,3 = askQS,8 0.0370 spr,4 = spr,9 0.0133 adep,4 = bdep,9 adepd,4 = bdepd,9 bdep,4 = adep,9 bdepd,4 = adepd,9 0.0920 vol,4 = vol,9 0.0133B a n i o n a l askQS,4 = bidQS,9 bidQS,4 = askQS,9 0.0028 spr,5 = spr,10 0.1730 adep,5 = bdep,10 adepd,5 = bdepd,10 bdep,5 = adep,10 bdepd,5 = adepd,10 0.2337 vol,5 = vol,10 o f 0.999 l a n d P o askQS,5 = bidQS,10 bidQS,5 = askQS,10 0.1562

34

p - val : H0 : p - val : H0 : p - val :

t

k

Impact of the Explanatory Variables

the bid-ask spread, depth dummies, volatility and the quote slopes can be observed. The parameter estimates for the ask side of a market are much larger in value, which means that the immediate decisions to buy zloty (sell euro) are significantly more sensitive to liquidity or information motivated factors. From this viewpoint, our general and richly parameterized duration model can be fully justified.

spr,1 = spr,6 0.0031 adep,1 = bdep,6 adepd,1 = bdepd,6 bdep,1 = adep,6 bdepd,1 = adepd,6 0.0012 vol,1 = vol,6 0.0000 askQS,1 = bidQS,6 bidQS,1 = askQS,6 0.0000 spr,2 = spr,7 0.0001 adep,2 = bdep,7 adepd,2 = bdepd,7 bdep,2 = adep,7 bdepd,2 = adepd,7 0.1150 vol,2 = vol,7 0.0064 askQS,2 = bidQS,7 bidQS,2 = askQS,7 0.0060 spr,3 = spr,8 0.0108 adep,3 = bdep,8 adepd,3 = bdep,8 bdep,3 = adep,8 bdepd,3 = adep,8 0.0794 vol,3 = vol,8 0.0108 askQS,3 = bidQS,8 bidQS,3 = askQS,8 0.0370 spr,4 = spr,9 0.0133 adep,4 = bdep,9 adepd,4 = bdepd,9 bdep,4 = adep,9 bdepd,4 = adepd,9 0.0920 vol,4 = vol,9 0.0133 askQS,4 = bidQS,9 bidQS,4 = askQS,9 0.0028 spr,5 = spr,10 0.1730 adep,5 = bdep,10 adepd,5 = bdepd,10 bdep,5 = adep,10 bdepd,5 = adepd,10 0.2337 vol,5 = vol,10 0.999 askQS,5 = bidQS,10 bidQS,5 = askQS,10 0.1562

H0 : p - val : H0 :

p - val : H0 : p - val : H0 : p - val :

Table 4: Symmetry restrictions ­ results from the likelihood ratio test.

7

Conclusions

This paper contributes to the literature on order dynamics in two main aspects. We generalize the asymmetric ACD model of Bauwens & Giot (2003) to the case when there are more than two competing risks. The obtained multistate ACD model can serve as a flexible tool for description of expected durations, at the end of which particular events (i.e. states defined on a "micro scale" by appropriate thinning the data) can take place. In our model the selected events correspond to submissions or cancellations of orders attributed to particular order classes. The model describes the bivariate density for durations (time intervals between selected orders) and the corresponding event classes (discrete variables indicating the type of an event). Thus, it can account for the very complex dynamics inherent to the order-driven market. As the time variable plays first fiddle, the model describes the pace of dealer activities when confronted with actions taken by other market participants. We also show how to simulate data from the multistate ACD specification thus enabling a more detailed insight into the data generating process. In the empirical analysis we use data for the EUR/PLN currency pair from a very popular interbank trading venue: the Reuters Dealing 3000 Spot Matching System. To our knowledge this is the first study that investigates trader preference with regard to order choices within the emerging currency markets. We establish the most probable sequence according to which orders classified to selected classes arrive to the market or are withdrawn from it. We identify market 33

6

WORKING PAPER No. 104

35

p - val : H0 : p - val : H0 : p - val :

adepd,1 = bdepd,6 bdep,1 = adep,6 bdepd,1 = adepd,6 0.0012 vol,1 = vol,6 0.0000 askQS,1 = bidQS,6 bidQS,1 = askQS,6 0.0000

adepd,2 = bdepd,7 bdep,2 = adep,7 bdepd,2 = adepd,7 0.1150 vol,2 = vol,7 0.0064 askQS,2 = bidQS,7 bidQS,2 = askQS,7 0.0060

adepd,3 = bdep,8 bdep,3 = adep,8 bdepd,3 = adep,8 0.0794 vol,3 = vol,8 0.0108 askQS,3 = bidQS,8 bidQS,3 = askQS,8 0.0370

adepd,4 = bdepd,9 bdep,4 = adep,9 bdepd,4 = adepd,9 0.0920 vol,4 = vol,9 0.0133 askQS,4 = bidQS,9 bidQS,4 = askQS,9 0.0028

adepd,5 = bdepd,10 bdep,5 = adep,10 bdepd,5 = adepd,10 0.2337 Conclusions vol,5 = vol,10 0.999 askQS,5 = bidQS,10 bidQS,5 = askQS,10 0.1562

Table 4: Symmetry restrictions ­ results from the likelihood ratio test.

7

Conclusions

This paper contributes to the literature on order dynamics in two main aspects. We generalize the asymmetric ACD model of Bauwens & Giot (2003) to the case when there are more than two competing risks. The obtained multistate ACD model can serve as a flexible tool for description of expected durations, at the end of which particular events (i.e. states defined on a "micro scale" by appropriate thinning the data) can take place. In our model the selected events correspond to submissions or cancellations of orders attributed to particular order classes. The model describes the bivariate density for durations (time intervals between selected orders) and the corresponding event classes (discrete variables indicating the type of an event). Thus, it can account for the very complex dynamics inherent to the order-driven market. As the time variable plays first fiddle, the model describes the pace of dealer activities when confronted with actions taken by other market participants. We also show how to simulate data from the multistate ACD specification thus enabling a more detailed insight into the data generating process. In the empirical analysis we use data for the EUR/PLN currency pair from a very popular interbank trading venue: the Reuters Dealing 3000 Spot Matching System. To our knowledge this is the first study that investigates trader preference with regard to order choices within the emerging currency markets. We establish the most probable sequence according to which orders classified to selected classes arrive to the market or are withdrawn from it. We identify market microstructure factors that exert an influence on the expected time until a given event takes place. Our results verify selected hypotheses on determinants of order 33 choice and their timing in limit order markets. As the results we obtained are quite extensive, we will restrict ourselves to those that refer to the hypotheses stated in the section 2. The hypotheses (1-4) have been supported. The limit sells (buys) are more probable after market buys (sells) than after market sells (buys). Market orders submitted on the same side cluster together thus the sequence buy-buy (sell-sell) is more probable than buy-sell or sell-buy. Large depth visible on one side of the market enhances more inside-the-quote orders placed on the same side of the order book as is predicted by Hall & Hautsch (2006) and Anand et al. (2005). The same also accounts for aggressive market orders on both market sides, which can be explained by the "enhancement effect" or the "short-term forecasting effect". The bid-ask spread decreases the pace of market order submissions and increases the arrival rate of limit orders (see Biais (1995); Harris (1998); Bae et al. (2003); Ranaldo (2004); Ellul et al. (2007) and Lo & Sapp (2008)). The increase in market uncertainty, proxied by the realized volatility, prompts market orders (especially theses to buy euro and to sell zloty) and decreases the number of best limit orders. Order cancellations take place mostly after the submission of best orders on the same market side, which may be perceived as a signal of spoofing. We do not find support for hypotheses (6-7). A decrease in the bid-ask spread does not initiate submission of best limit orders. On N a t i n a l B a n k P o l a ­ the contrary, they are cancelled if the bid-ask spread iso large, although o­ f possibly n d they will be resubmitted at a new and better price. An increase in volatility does not have a statistically significant impact on order cancellations.

7

36

Conclusions

decreases the pace of market order submissions and increases the arrival rate of limit orders (see Biais (1995); Harris (1998); Bae et al. (2003); Ranaldo (2004); Ellul et al. (2007) and Lo & Sapp (2008)). The increase in market uncertainty, proxied by the realized volatility, prompts market orders (especially theses to buy euro and to sell zloty) and decreases the number of best limit orders. Order cancellations take place mostly after the submission of best orders on the same market side, which may be perceived as a signal of spoofing. We do not find support for hypotheses (6-7). A decrease in the bid-ask spread does not initiate submission of best limit orders. On the contrary, they are cancelled if the bid-ask spread is large, although ­ possibly ­ they will be resubmitted at a new and better price. An increase in volatility does not have a statistically significant impact on order cancellations. There are many possible extensions for our empirical study. The model can be easily extended to more than ten competing risks and the multistate ACD model can also be widely used in order to study other market events defined on the "micro-scale" (trades of different volume, price changes of different size, submissions of hidden orders called "iceberg orders", or the use of algo trading). If the events can be reflected as an ordered point process, there is a large spectrum of possible economic enquiries that can be investigated in this competing risk framework.

34

7

WORKING PAPER No. 104

37

References

References

Admati, A. & P. Pfleiderer (1988): "A Theory of Intra-Day Patterns: Volume and Price Variability," Review of Financial Studies, 1, 3­40. Anand, A., S. Chakravarty, & T. Martell (2005): "Empirical Evidence on the Evolution of Liquidity: Choice of Market versus Limit Orders by Informed and Uninformed Traders," Journal of Financial Markets, 8, 289­309. Bae, K.-H., H. Jang, & K. Park (2003): "Traders' Choice between Limit and Market Orders: Evidence from NYSE Stocks," Journal of Financial Markets, 6, 517­538. Bauwens, L. & P. Giot (2000): "The Logarithmic ACD Model: An Application to the Bid/Ask Quote Process of two NYSE Stocks," Annales d'Economie et de Statistique, 60, 117­149. ---- (2003): "Asymmetric ACD Models: Introducing Price Information in ACD Models," Empirical Economics. Bauwens, L. & D. Veredas (2004): "The Stochastic Conditional Duration Model: A Latent Factor Model for the Analysis of Financial Durations," Journal of Econometrics. Bauwens, L., F. Galli, & P. Giot (2008): "The Moments of Log-ACD Models," Quantitative and Qualitative Analysis in Social Sciences, 2, 1­28. Biais, B. (1995): "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," The Journal of Finance, 50, 1655­1689. Bloomfeld, R., M. O'Hara, & G. Saar (2005): "The 'Make or Take' Decision in an Electronic Market: Evidence on an Evolution of Liquidity," Journal of Financial Economics, 75, 165­199. Diamond, D. & R. Verrecchia (1987): "Constraints on Short-Selling and Asset Price Adjustment to Private Information," Journal of Financial Economics, 18, 277­311. Easley, D. & M. O'Hara (1992): "Time and the Process of Security Price Adjustment," Journal of Finance, 47, 577­607. Ellul, A., C. Holden, P. Jain, & R. Jennings (2007): "Order Dynamics: Recent Evidence from the NYSE," Journal of Empirical Finance, 14, 636­661.

Engle, R. F. & J. R. Russell (1998): "Autoregressive Conditional Duration: A 35 New Model for Irregularly Spaced Transaction Data," Econometrica, 66, 1127­ 1162.

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Fong, K. & W.-M. Liu (2010): "Limit Order Revisions," Journal of Banking and N a t i o n a l B a n k o f P o l a n d Finance, 1873­1885. Foucault, T. (1999): "Order Flow Composition and Trading Costs in a Dynamic

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Engle, R. F. & J. R. Russell (1998): "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, 66, 1127­ 1162. Fong, K. & W.-M. Liu (2010): "Limit Order Revisions," Journal of Banking and Finance, 1873­1885. Foucault, T. (1999): "Order Flow Composition and Trading Costs in a Dynamic Limit Order Market," Journal of Financial Markets, 2, 99­134. Foucault, T., O. Kadan, & E. Kandel (2005): "Limit Order Book as a Market for Liquidity," Review of Financial Studies, 18, 1171­1217. Glosten, L. R. (1994): "Is the Electronic Open Limit Order Book Inevitable?" The Journal of Finance, 49 (4), 1127­1161. Goettler, R., C. Parlour, & U. Rajan (2005): "Equillibrium in a Dynamic Limit Order Market," Journal of Finance, 60, 2149­2192. Hall, A. & N. Hautsch (2006): "Order Aggressiveness and Order Book Dynamics," Empirical Economics, 30, 973­1005. ---- (2007): "Modelling the Buy and Sell Intensity in a Limit Order Book," Journal of Financial Markets, 10, 249­286. Handa, P. & R. Schwartz (1996): "Limit Order Trading," Journal of Finance, 51, 1835­1861. Harris, L. E. (1998): "Optimal Order Submission Strategies in Some Stylized Trading Problems," Financial Markets, Institutions and Instruments, 7, 149­ 178. Hasbrouck, J. & G. Saar (2009): "Technology and Liquidity Provision: The Blurring of Traditional Definitions," Journal of Financial Markets, 12 (2), 143­ 172. Liu, W.-M. (2009): "Monitoring and Limit Order Submission Risks," Journal of Financial Markets, 107­141. Lo, I. & S. Sapp (2008): "The Submission of Limit Orders or Market Orders: The Role of Timing and Information in the Reuters D2000-2 System," Journal of International Money and Finance, 27, 1056­1073. Osler, C. (2003): "Currency Orders and36 Exchange Rate Dynamics: an Explanation for the Predictive Success of Technical Analysis." Journal of Finance, 1791­ 1819. Parlour, C. (1998): "Price Dynamics in Limit Order Markets," Review of Financial Studies, 11, 789­816. Pascual, A. & D. Veredas (2004): "What Pieces of Limit Order Book Information are Informative?" Journal of Financial Markets, 7, 53­74.

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Osler, C. (2003): "Currency Orders and Exchange Rate Dynamics: an Explanation References for the Predictive Success of Technical Analysis." Journal of Finance, 1791­ 1819. Parlour, C. (1998): "Price Dynamics in Limit Order Markets," Review of Financial Studies, 11, 789­816. Pascual, A. & D. Veredas (2004): "What Pieces of Limit Order Book Information are Informative?" Journal of Financial Markets, 7, 53­74. Ranaldo, A. (2004): "Order Aggresiveness in Limit Order Book Markets," Journal of Financial Markets, 7, 53­74. Rosu, I. (2009): "A Dynamic Model for the Limit Order Book," Review of Financial Studies, 22, 4601­4641. Seppi, D. J. (1997): "Liquidity Provision with Limit Orders and a Strategic Specialist," Review of Financial Studies, 10, 103­150. Verhoeven, P., S. Ching, & H. Ng (2003): "Determinants of the Decision to Submit Market or Limit Orders on the ASX," Pacific-Basin Finance Journal, 12, 1­18. Yeo, W. (2002): "Persistent Pattern in Limit Order Submission," Working Paper, Indiana University.

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Appendix

A

Appendix

I. Properties of the Weibull distribution. The Weibull density for the variable i , with parameters > 0, c = 1 (i.e. under the restriction that the dispersion parameter is equal to 1) is: fi (i ) = (i )-1 exp(- ) i and the survival function is: Si (i ) = exp(- ) i i.e. i W (1, ). The expectation of the Weibull distribution is: µi = (1 + -1 ) (12) (11) (10)

II. Main properties of the MAACD model. Under the framework of the standard ACD model of (Engle & Russell (1998)), a -1 duration xi,k can be depicted as: xi,k = i,k i,k , where i,k = i,k · {(1 + k )}-1 , i,k = E(xi,k |Fi-1 ) and E(i,k |Fi-1 ) = 0. The density and survival functions of xi,k can be given as: fxi,k (xi,k ) = 1 xi,k fi,k i,k i,k xi,k i,k

k -1

(13) xi,k exp - i,k

k

k = i,k

Sxi,k (xi,k ) = Si,k

xi,k i,k

k

(14)

xi,k = exp - i,k

The conditional cumulative density function (CDF) for xi defined as xi = min{x1,i , ..., x10,i } can be derived as: F (xi |Fi-1 ) = 1 - P (Xi > xi |Fi-1 )

10

(15)

= 1-

k=1 10

P (xi,k > xi |Fi-1 ) Sxi,k

k=1

= 1- 38

xi i,k

WORKING PAPER No. 104

41

Appendix

The density function for xi can be obtained from the formula (16): 10 k -1 k 10 k xi F (xi ) xi · exp - = f (xi |Fi-1 ) = (17) xi i,k i,k i,k k=1 k=1 f (xi , yi |Fi-1 ) f (xi |Fi-1 ) 10 k

k=1 i,k

Therefore, after inserting the survival given in formula (14) into (15), we have: k 10 xi (16) F (xi |Fi-1 ) = 1 - exp - i,k k=1 10 k xi = 1 - exp - i,k k=1

The conditional (with respect to Fi-1 and current duration xi ) transition probabilities between the selected events are given as: f (yi |xi , Fi-1 ) = (18) k -1 Iik k xi · exp - xi i,k i,k

=

10

k=1

k k=1 i,k

=

10

k i,k

k -1 k 10 xi xi · k=1 exp - i,k i,k k -1 Iik k -1

xi i,k

Obviously, as in the case of the asymmetric ACD model, the yi and xi are not independent. The conditional (only with respect to Fi-1 and not the current duration xi ) transition probabilities do not have a closed analytic form and are equal to: -1 xi l 10 - xi k k P (yi = k|Fi-1 ) = e i,l dxi (19) · i,1 i,1 l=1

0

10

k k=1 i,k

xi i,k

Thus, yi and xi are independent.

Under the restriction k = for k = 1, 2, ..., 10, the formula 18 boils down to: 10 - Iik k=1 i,k f (yi |Fi-1 ) = (20) 10 - k=1 i,k 39

42

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