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# Papers

Below you will find a list of papers that discuss various issues related to the order-driven transactional data. If you run across a similar paper, please share it with fellow users by sending us the reference, and we will post a link to it here. Please help us build the most comprehensive and usable knowledge base on how to use transaction data in trading.

## The Market Impact of a Limit Order

Nikolaus Hautsch, Ruihong Huang
Despite their importance in modern electronic trading, virtually no systematic empirical evidence on the market impact of incoming orders is existing. We quantify the short-run and long-run price effect of posting a limit order by proposing a high-frequency cointegrated VAR model for ask and bid quotes and several levels of order book depth. Price impacts are estimated by means of appropriate impulse response functions. Analyzing order book data of 30 stocks traded at Euronext Amsterdam, we show that limit orders have significant market impacts and cause a dynamic (and typically asymmetric) rebalancing of the book. The strength and direction of quote and spread responses depend on the incoming orders’ aggressiveness, their size and the state of the book. We show that the effects are qualitatively quite stable across the market. Cross-sectional variations in the magnitudes of price impacts are well explained by the underlying trading frequency and relative tick size.

## Liquidity Shocks and Order Book Dynamics

Bruno Biais, Pierre-Olivier Weill
We propose a dynamic competitive equilibrium model of limit order trading, based on the premise that investors cannot monitor markets continuously. We study how limit order markets absorb transient liquidity shocks, which occur when a significant fraction of investors lose their willingness and ability to hold assets. We characterize the equilibrium dynamics of market prices, bid-ask spreads, order submissions and cancelations, as well as the volume and limit order book depth they generate.

## Trading Volume in Dealer Markets

Katya Malinova, Andreas Park
We develop a financial market trading model in the tradition of Glosten and Milgrom (1985) that allows us to incorporate non-trivial volume. We observe that in this model price volatility is positively related to the trading volume and to the absolute value of the net order flow, i.e. the order imbalance. Moreover, higher volume leads to higher order imbalances. These findings are consistent with well-established empirical findings. Our model further predicts that higher trader participation and systematic improvements in the quality of traders' information lead to higher volume, larger order imbalances, lower market depth, shorter duration, and higher price volatility.

## Order flow and exchange rate changes: A look at the NZD/USD and AUD/USD

Nick Smyth
In this paper, we apply a series of empirical microstructure tests to the NZD/USD and AUD/USD. In contrast to a more traditional macro approach to explaining exchange rate changes, microstructure studies focus on the role that transactions play in helping the market aggregate information on individual market participants expectations of economic fundamentals and risk preferences. Our data comes from the Reuters Spot Matching service, the main interbank trading platform in both currency pairs, and covers almost five and a half years of transactions from January 2001 to March 2006, a much longer and more representative time series than many empirical microstructure applications to date. We find that there is a strong contemporaneous relationship between net order flow (the net of buyerinitiated and seller-initiated transactions) and changes in the NZD/USD and AUD/USD at frequencies from one minute to one week, similar to studies on other currencies. We also find that cross-currency order flow has a positive association with changes in the other exchange rate (ie AUD/USD order flow has a positive contemporaneous relationship with changes in the NZD/USD). Finally, we examine a wide range of New Zealand, Australian and US data releases and central bank interest rate decisions and find that order flow plays an important role in communicating different interpretations of macroeconomic news.

## Characteristics of Observed Limit Order Demand and Supply Schedules for Individual Stocks

Jung-Wook Kim, Jason Lee, Randall Morck
Using complete order books from the Korea Stock Exchange for a four-year period including the 1997 Asian financial crisis, we observe (not estimate) limit order demand and supply curves for individual stocks. Both curves have demonstrably finite elasticities. These fall markedly, by about 40%, with the crisis and remain depressed long after other economic and financial variables revert to pre-crisis norms. Superimposed upon this common long-term modulation, individual stocks's supply and demand elasticities correlate negatively at high frequencies. That is, when a stock exhibits an unusually elastic demand curve, it tends simultaneously to exhibit an unusually inelastic supply curve, and vice versa. These findings have potential implications for modeling how information flows into and through stock markets, how limit order providers react or interact to information flows, how new information is capitalized into stock prices, and how financial crises alter these processes. We advance speculative hypotheses, and invite further theoretical and empirical work to explain these findings and their implications.

## The Information Content Of An Open Limit-Order Book

Charles Cao, Oliver Hansch, Xiaoxin Wang
Using data from the Australian Stock Exchange, the authors assess the information content of an open limit-order book with a particular focus on the incremental information contained in the limit orders behind the best bid and offer. The authors find that the order book is moderately informative—its contribution to price discovery is approximately 22%. The remaining 78% is from the best bid and offer prices on the book and the last transaction price. Furthermore, the authors find that order imbalances between the demand and supply schedules along the book are significantly related to future short-term returns, even after controlling for the autocorrelations in return, the inside spread, and the trade imbalance.

## A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects

Hurvich, Clifford and Wang, Yi
We propose a new transaction-level bivariate log-price model, which yields fractional or standard cointegration. The model provides a link between market microstructure and lower-frequency observations. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times between trades, and a pair of stationary noise processes which determine the jump sizes in the pure-jump log-price process. Our model includes feedback between the disturbances of the two log-price series at the transaction level, which induces standard or fractional cointegration for any fixed sampling interval. We prove that the cointegrating parameter can be consistently estimated by the ordinary least-squares estimator, and obtain a lower bound on the rate of convergence. We propose transaction-level method-of-moments estimators of the other parameters in our model and discuss the consistency of these estimators. We then use simulations to argue that suitably-modified versions of our model are able to capture a variety of additional properties and stylized facts, including leverage, and portfolio return autocorrelation due to nonsynchronous trading. The ability of the model to capture these effects stems in most cases from the fact that the model treats the (stochastic) intertrade durations in a fully endogenous way.

## Predicting Stock Volatility Using After-Hours Information

Chun-Hung Chen, Wei-Choun Yu, Eric Zivot
We use realized volatilities based on after hours high frequency returns to predict next day volatility. We extend GARCH and long-memory forecasting models to include additional information: the whole night, the preopen, the postclose realized variance, and the overnight squared return. For four NASDAQ stocks (MSFT, AMGN, CSCO, and YHOO) we find that the inclusion of the preopen variance can improve the out-of-sample forecastability of the next day conditional day volatility. Additionally, we find that the postclose variance and the overnight squared return do not provide any predictive power for the next day conditional volatility. Our findings support the results of prior studies that traders trade for non-information reasons in the postclose period and trade for information reasons in the preopen period.

## Time-Deformation Modeling Of Stock Returns Directed By Duration Processes

Dingan Feng, Peter X.-K. Song, Tony S. Wirjanto
This paper presents a new class of time-deformation (or stochastic volatility) models for stock returns sampled in transaction time and directed by a generalized duration process. Stochastic volatility in this model is driven by an observed duration process and a latent autoregressive process. Parameter estimation in the model is carried out by using the method of simulated moments (MSM) due to its analytical feasibility and numerical stability for the proposed model. Simulations are conducted to validate the choices of the moments used in the formulation of the MSM. Both the simulation and empirical results obtained in this paper indicate that this approach works well for the proposed model. The main empirical findings for the IBM transaction return data can be summarized as follows: (i) the return distribution conditional on the duration process is not Gaussian, even though the duration process itself can marginally function as a directing process; (ii) the return process is highly leveraged; (iii) a longer trade duration tends to be associated with a higher return volatility; and (iv) the proposed model is capable of reproducing return whose marginal density function is close to that of the empirical return.

## The interday and intraday patterns of the overnight market - evidence from an electronic platform

Renaud Beaupain, Alain Durré
This paper examines the interday and intraday dynamics of the euro area overnight money market on the basis of an original set of market activity and liquidity proxies constructed from both pre- and post-trade data. The empirical literature provides extensive evidence supporting the rejection of the martingale hypothesis both between days and within days, primarily for interest rates and volatility. We extend this analysis and investigate the seasonality of market activity and liquidity in a market dominated by utilitarian traders. We provide evidence that the Eurosystem's operational framework and calendar effects cause the observed regular patterns. We additionally show that utilitarian trading intensifies at the turn of the reserve maintenance period. The increased un-certainty associated with greater information asymmetry between market participants when reserve requirements become binding lead to a deterioration of market liquidity. Our analysis additionally turns out to be sensitive to the implementation in March 2004 of structural changes to the operational framework and to the more frequent occurrence of fine-tuning operations since October 2004.

Dale W.R. Rosenthal
The problem of classifying trades as buys or sells is examined. I propose estimated quotes for midpoint and bid/ask tests and a modeling approach to classification. Prevailing quotes are estimated using flexible approximations to the distribution for delays of quotes relative to trade timestamps. Classification is done by a generalized linear model which includes improved versions of midpoint, tick, and bid/ask tests. The model also considers the relative strengths of these tests, can account for market microstructure peculiarities, and allows for autocorrelations and cross-correlations in trade direction. The correlation modeling corrects for pseudoreplication, yielding more accurate standard errors and fixed effect estimates. Further, the model estimates probabilities of correct classification. The model is compared to various trade classification methods using a sample of 2,836 domestic US stocks from an unexplored, recent, and readily-available dataset. Out of sample, modeled classifications are 1-2% more accurate overall than current methods; this improvement is consistent across dates, sectors, and locations relative to the inside quote. For Nasdaq and NYSE stocks, 1% and 1.3% of the improvement comes from using relative strengths of the various tests; 0.9% and 0.7% of the improvement, respectively, comes from using some form of estimated quotes. For AMEX stocks, a 0.4% improvement is attributed to using a lagged version of the bid/ask test. I also find indications of short- and ultra-short-term alpha.

## Duration and Order Type Clusters

Wing Lon NG
This paper introduces a new bivariate autoregressive conditional framework (ACDÃ—ACL) for modelling the arrival process of buy and sell orders in a limit order book. The model contains two dynamic components to describe the observed clustering of durations and order types: a duration process to capture the time structure, combined with a new "Autoregressive Conditional Logit" model in order to display the traders' order choice. Both processes are adapted to a common natural filtration and modelled simultaneously. It can be shown that the state of the order book as well as the success and the speed of the matching process have a significant influence on the traders' decisions when and on which side of the market to submit orders and, thus, affect the market's liquidity

## Analysis of Limit Order Book and Order Flow

Nuttawat Visaltanachoti, Charlie Charoenwong and David Ding
This paper extensively employs the order and trade data to analyze the shape of limit order book and the behavior of strategic order submission. The order book of stocks exhibits weakly convex pattern on the bid side due to wide price spreads away from the market. This characteristic of liquidity is particularly strong for the small stocks with large minimum tick size. In addition, the same order type occurs more frequently after the event had occurred than it would unconditionally. This diagonal effect is not fully explained by the order splitting. Moreover, the determinants driving order aggressiveness include bid-ask spread, market depths, other price spreads and depths away from the market, and market sentiment. Responding to the limit order book movement, an order aggressiveness revision behavior of market order traders is opposite to limit order traders, and contrarian traders react stronger than momentum traders.

## Critical comparison of several order-book models for stock-market fluctuations

Frantisek Slanina
Far-from-equilibrium models of interacting particles in one dimension are used as a basis for modelling the stock-market fluctuations. Particle types and their positions are interpreted as buy and sell orders placed on a price axis in the order book. We revisit some modifications of well-known models, starting with the Bak-Paczuski-Shubik model. We look at the four decades old Stigler model and investigate its variants. One of them is the simplified version of the Genoa artificial market. The list of studied models is completed by the models of Maslov and Daniels et al. Generically, in all cases we compare the return distribution, absolute return autocorrelation and the value of the Hurst exponent. It turns out that none of the models reproduces satisfactorily all the empirical data, but the most promising candidates for further development are the Genoa artificial market and the Maslov model with moderate order evaporation.

## Order Placement Strategies in a Pure Limit Order Book Market

Charles Cao, Oliver Hansch and Xiaoxin Wang
Using order book information from the Australian Stock Exchange, we examine whether (and to what extent) the order book affects investors’ order placement strategies. We find that the top of the book always affects order submissions, cancellations and amendments, while the rest of the book mostly contributes to the decision of order cancellations and amendments. The previously documented order submission aggressiveness, given a crowded first step of the book, persists over to other price steps, and is also found in order amendments and cancellations along the book. Finally, investors tend to fill in the large price gaps in the book by submitting or amending orders.

## Empirical regularities of order placement in the Chinese stock market

Gao-Feng Gu, Wei Chen, Wei-Xing Zhou
Using ultra-high-frequency data extracted from the order flows of 23 stocks traded on the Shenzhen Stock Exchange, we study the empirical regularities of order placement in the opening call auction, cool period and continuous auction. The distributions of relative logarithmic prices against reference prices in the three time periods are qualitatively the same with quantitative discrepancies. The order placement behavior is asymmetric between buyers and sellers and between the inside-the-book orders and outside-the-book orders. In addition, the conditional distributions of relative prices in the continuous auction are independent of the bid-ask spread and volatility. These findings are crucial to build an empirical behavioral microscopic model based on order flows for Chinese stocks.

## The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows

Carl Chiarella, Giulia Iori, Josep Perello
In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components to the expectation of future asset returns, namely-fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book.

Xiao-Hui Ni, Wei-Xing Zhou
We use high-frequency data of 1364 Chinese A-share stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange to investigate the intraday patterns in the bid-ask spreads. The daily periodicity in the spread time series is confirmed by Lomb analysis and the intraday bid-ask spreads are found to exhibit $L$-shaped pattern with idiosyncratic fine structure. The intraday spread of individual stocks relaxes as a power law within the first hour of the continuous double auction from 9:30AM to 10:30AM with exponents $\beta_{\rm{SHSE}}=0.19\pm0.069$ for the Shanghai market and $\beta_{\rm{SZSE}}=0.18\pm0.067$ for the Shenzhen market. The power-law relaxation exponent $\beta$ of individual stocks is roughly normally distributed. There is evidence showing that the accumulation of information widening the spread is an endogenous process.

## An empirical behavioral model of liquidity and volatility

Szabolcs Mike, J. Doyne Farmer
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are validated against real data. Our empirical studies of order flow uncover several interesting regularities in the way trading orders are placed and cancelled. The resulting simple model of order flow is used to simulate price formation under a continuous double auction, and the statistical properties of the resulting simulated sequence of prices are compared to those of real data. The model is constructed using one stock (AZN) and tested on 24 other stocks. For low volatility, small tick size stocks (called Group I) the predictions are very good, but for stocks outside Group I they are not good. For Group I, the model predicts the correct magnitude and functional form of the distribution of the volatility and the bid-ask spread, without adjusting any parameters based on prices. This suggests that at least for Group I stocks, the volatility and heavy tails of prices are related to market microstructure effects, and supports the hypothesis that, at least on short time scales, the large fluctuations of absolute returns are well described by a power law with an exponent that varies from stock to stock.

## Do Stylised Facts of Order Book Markets Need Strategic Behaviour?

This paper studies the role of strategy and the order book market mechanism in price dynamics and the order flow behaviour. To this end we analyse a zero-intelligence agent model of a dynamic limit order market. Stylised facts of limit order markets are shown to be influenced and, in some cases, governed by the market mechanism rather than strategic interaction. Positive correlation in order types, for instance, is the result of the market architecture, and price movements may be predicted in the short term from analysing the state of the order book. In contrast the absolute probabilities of order submission highlight the contribution of strategic behaviour.

## The limit order book on different time scales

Zoltan Eisler, Janos Kertesz, Fabrizio Lillo
Financial markets can be described on several time scales. We use data from the limit order book of the London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more systematic global behavior.

## Competition in the Market for NASDAQ Securities

Michael A. Goldstein, Andriy V. Shkilko, Robert A. Van Ness, and Bonnie F. Van Ness
The study investigates competition in the market for NASDAQ stocks during a recent period in U.S. equity markets history when three major ECNs  Archipelago, Island, and Instinet  are identifiable in TAQ. We show that the ECNs compete with NASDAQ's SuperMontage on the basis of quotes, execution times, and costs. The three ECNs differ due to uniqueness of their limit order books, cost schedules, and heterogeneity of trading clienteles. Informed traders are shown to prefer venues with sufficient liquidity over those that guarantee anonymity of executions. Despite high levels of segmentation, uneven regulation, and controversial order attraction practices, quote competitiveness is found to increase the probability of executions on all four venues.

## Order Aggressiveness and Quantity: How Are They Determined in a Limit Order Market?

Ingrid Lo, Stephen G. Sapp
Dealers trading in a limit order market must choose both the order aggressiveness and the quantity for their orders. We empirically investigate how dealers jointly make these decisions in the foreign exchange market using a unique simultaneous equations model. The model uses an ordered probit model to account for the discrete nature of order aggressiveness and a censored regression model to capture the clustering of orders placed at the smallest available quantity, \$1 million. We find evidence of a clear trade-off between order aggressiveness and quantity: more aggressive orders tend to be smaller in size. The increased competition (demand) suggested by increased depth on the same (opposite) side of the market leads to less (more) aggressive orders in smaller (larger) size. This holds for the depths at both the best and off-best prices, even though off-best depths are not observable to dealers.

## Does the open limit order book matter in explaining long run volatility

Roberto PASCUAL and David Veredas
This paper evaluates the informational content of an open limit order book by studying its role in explaining long run volatility. We separate liquidity-driven (transitory) volatility from information-driven (long run) volatility using a dynamic state-space co-integration model for ask and bid quotes. We report that changes in immediacy costs precede posterior fluctuations in long run volatility even after controlling for the incoming order flow. The book is less informative for large-caps than for small-caps. Consistently with previous studies, the book beyond the best quotes adds explanatory power to the best quotes. Finally, the explanatory power of the book decreases with the time resolution of the analysis.

## Does the Open Limit Order Book Matter in Explaining Long Run Volatility?

Roberto Pascual, David Veredas
This paper evaluates the informational content of an open limit order book by studying its role in explaining long run volatility. We separate liquidity-driven (transitory) volatility from information-driven (long run) volatility using a dynamic state-space co-integration model for ask and bid quotes. We report that changes in immediacy costs precede posterior fluctuations in long run volatility even after controlling for the incoming order flow. The book is less informative for large-caps than for small-caps. Consistently with previous studies, the book beyond the best quotes adds explanatory power to the best quotes. Finally, the explanatory power of the book decreases with the time resolution of the analysis.

## Transaction-Data Analysis of Marked Durations and Their Implications for Market Microstructure

Anthony S Tay, Christopher Ting, Y. K. Tse and Mitch Warachka
We propose an Autoregressive Conditional Marked Duration (ACMD) model for the analysis of irregularly spaced transaction data. Based on the Autoregressive Conditional Duration (ACD) model, the ACMD model assigns marks to characterize events such as tick movements and trade directions (buy/sell). Applying the ACMD model to tick movements, we study the influence of trade frequency, direction and size on price dynamics, volatility and the permanent and transitory price impacts of trade. We also apply the ACMD model to analyze trade-direction data and estimate the probability of informed trading (PIN). We find that trade frequency has a critical role in price dynamics while the contribution of volume to price impacts, volatility, and the probability of informed trading is marginal.

## Does the Open Limit Order Book Reveal Information About Short-run Stock Price Movements?

Hellström, Jörgen, Simonsen, Ola
This paper empirically tests whether an open limit order book contains information about future short-run stock price movements. To account for the discrete nature of price changes, the integer-valued autoregressive model of order one is utilized. A model transformation has an advantage over conventional count data approaches since it handles negative integer-valued price changes. The empirical results reveal that measures capturing offered quantities of a share at the best bid- and ask-price reveal more information about future short-run price movements than measures capturing the quantities offered at prices below and above. Imbalance and changes in offered quantities at prices below and above the best bid- and ask-price do, however, have a small and significant effect on future price changes. The results also indicate that the value of order book information is short-term.

## Models and Properties of Financial Limit Order Books

Unknown
This paper presented simulations of a simple order book model, which recovered some generic features of the real price process.

## Locked and Crossed Markets on NASDAQ and the NYSE

Andriy V. Shkilko, Bonnie F. Van Ness, Robert A. Van Ness
The NBBO for an average active stock is non-positive (locked or crossed) 10.58% and 4.05% of the time on, respectively, the NASDAQ and the NYSE inter-markets. Locks and crosses are frequent fleeting events that usually accompany significant price changes. Non-positive NBBOs arise because of (i) simultaneous and (ii) tardy quote updates, (iii) electronically unreachable quotes, (iv) reluctance to trade against autoquotes, (v) order transit considerations, and (vi) ECN liquidity attraction efforts. Most locks and crosses result from competitive trading practices in contemporary fragmented markets.

Nikolai Zaitsev
Microstructure of market dynamics is studied through analysis of tick price data. Linear trend is introduced as a tool for such analysis. Trend arbitrage inequality is developed and tested. The inequality sets limiting relationship between trend, bid-ask spread, market reaction and average update frequency of price information. Average time of market reaction is measured from market data. This parameter is interpreted as a constant value of the stock exchange and is attributed to the latency of exchange reaction to actions of traders. This latency and cost of trade are shown to be the main limit of bid-ask spread. Data analysis also suggests some relationships between trend, bid-ask spread and average frequency of price update process.

## The Next Tick on Nasdaq: Does Level II Information Matter?

Bruce Mizrach
The Nasdaq stock market provides information about buying and selling interest in what is called the Level II display. Using a bivariate VAR model of trades and quotes, I assess the effect of Level II prices and depths on short-run quote dynamics. I also determine the influence of individual market makers and electronic networks and find evidence of strategic behavior. Finally, I produce a set of dynamic market price responses to buy and sell orders, and I find that these estimates vary with standard measures of liquidity.

## Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets

Matthieu Wyart, Jean-Philippe Bouchaud, Julien Kockelkoren, Marc Potters, Michele Vettorazzo
We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid-ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility_per trade_, with R^2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatilitycomes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the nyse, a liquid market with specialists, where monopoly rents appear to be present.

## A Structural Error-Correction Model of Best Prices and Depths in the Foreign Exchange Limit Order Market

Ingrid Lo and Stephen G. Sapp
Traders using the electronic limit order book in the foreign exchange market can watch the posted price and depth of the best quotes change over the day. The authors use a structural errorcorrection model to examine the dynamics of the relationship between the best bid price, the best ask price, and their associated depths. They incorporate measures of the market depth behind the best quotes as regressors. They report four main findings. First, best prices and their associated depths are contemporaneously related to each other. More specifically, an increase in the ask (bid) price is associated with a drop (rise) in the ask (bid) depth. This suggests that sell traders avoid the adverse-selection risk of selling in a rising market. Second, when the spread-the error-correction term-widens, the bid price rises and the ask price drops, returning the spread to its long-term equilibrium value. Further, the best depth on both sides of the market drops, due to increased market uncertainty. Third, the lagged best depth impacts the price discovery on both sides of the market, with the effect being strongest on the same side of the market. Fourth, changes in the depth behind the best quotes impact both the best prices and quantities, even though those changes are unobservable to market participants.

Wee, Marvin

## Order Submission: The Choice between Limit and Market Orders

Ingrid Lo, Stephen G. Sapp
Most financial markets allow investors to submit both limit and market orders, but it is not always clear what affects the choice of order type. The authors empirically investigate how the time between order submissions, changes in the state of the order book, and price uncertainty influence the rate of submission of limit and market orders. The authors measure the expected time (duration) between the submissions of orders of each type using an asymmetric autoregressive conditional duration model. They find that the execution of market orders, as well as changes in the level of price uncertainty and market depth, impact the submissions of both best limit orders and market orders. After correcting for these factors, the authors also find differences in behaviour around market openings, closings, and unexpected events that may be related to changes in information flows at these times. In general, traders use more market (limit) orders at times when execution risk for limit orders is highest or the risk of unexpected price movements is highest.

## A Dynamic Model of the Limit Order Book

Ioanid Rosu
I propose a continuous-time model of price formation in a market where trading is conducted according to a limit-order book. Strategic liquidity traders arrive randomly in the market and dynamically choose between limit and market orders, trading off execution price with waiting costs. I prove the existence of a Markov equilibrium in which the bid and ask prices depend only on the numbers of buy and sell orders in the book, and which can be characterized in closed-form in several cases of interest. The model generates empirically verified implications for the shape of the limit-order book and the dynamics of prices and trades. In particular, I show that buy and sell orders can cluster away from the bid-ask spread, thus generating a hump-shaped limit-order book. Also, consistent with Dufour and Engle (2000), if the time duration between trades decreases, the price impact of trades increases. Finally, following a market buy order, both the ask and bid prices increase, with the ask increasing more than the bid - hence the spread widens.

## There's more to volatility than volume

Laszlo Gillemot, J. Doyne Farmer, Fabrizio Lillo
It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading, which cause both clustered volatility and heavy tails in price returns. We investigate this hypothesis using tick by tick data from the New York and London Stock Exchanges and show that only a small fraction of volatility fluctuations are explained in this manner. Clustered volatility is still very strong even if price changes are recorded on intervals in which the total transaction volume or number of transactions is held constant. In addition the distribution of price returns conditioned on volume or transaction frequency being held constant is similar to that in real time, making it clear that neither of these are the principal cause of heavy tails in price returns. We analyze recent results of Ane and Geman (2000) and Gabaix et al. (2003), and discuss the reasons why their conclusions differ from ours. Based on a cross-sectional analysis we show that the long-memory of volatility is dominated by factors other than transaction frequency or total trading volume.

## An empirical behavioral model of price formation

Szabolcs Mike, J. Doyne Farmer
Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step in this direction by developing empirical models that capture behavioral regularities in trading order placement and cancellation using data from the London Stock Exchange. For order placement we show that the probability of placing an order at a given price is well approximated by a Student distribution with less than two degrees of freedom, centered on the best quoted price. This result is surprising because it implies that trading order placement is symmetric, independent of the bid-ask spread, and the same for buying and selling. We also develop a crude but simple cancellation model that depends on the position of an order relative to the best price and the imbalance between buying and selling orders in the limit order book. These results are combined to construct a stochastic representative agent model, in which the orders and cancellations are described in terms of conditional probability distributions. This model is used to simulate price formation and the results are compared to real data from the London Stock Exchange. Without adjusting any parameters based on price data, the model produces good predictions for the magnitude and functional form of the distribution of returns and the bid-ask spread.

## Liquidity And Information Around Annual Earnings Announcements: An Intraday Analysis Of The Spanish Stock Market

David Abad, José Yagüe, Sonia Sanabria
This paper analyses the intraday reaction of the Spanish market to annual earnings announcements. Specifically, we examine the levels of stock liquidity, trading activity, volatility, and asymmetric information, as well as the order placement strategy around earnings disclosures. We also analyse the differences in the market reaction to announcements made during trading and non-trading hours. We find that stock liquidity and trading activity significantly improves after the announcement, although we do not find a significant reduction in the level of asymmetric information. Our results indicate that the stock market reaction differs according to the timing of the announcement. For overnight announcements, where investors have time to evaluate the earnings news before the market opens, the improvement in liquidity is immediate, caused by higher trading activity and less asymmetric information. On the contrary, for earnings announcements released when the market is open, the significant improvement in stock liquidity is observed after about one and a half hours of trading. The latter possibly occurs once informational advantages of investors who have superior information-processing abilities disappear, and therefore the level of asymmetric information decreases. The different reaction of the market to overnight and to daytime disclosures could explain the fact that Spanish firms prefer to release the announcement in trading (non-trading) hours when actual earnings are lower (higher) than forecast earnings.

## Does Order Flow Fragmentation Impact Market Quality? The Case of Nasdaq SuperMontage

Kheira BENHAMI and Christophe BISIÈRE
On December 2002, The Nasdaq Stock Market completed the roll out of its new trading platform SuperMontage. It was initially conceived to centralize the order flow for Nasdaq stocks. However, Island, one of the biggest ECN, decided not to participate to the montage and stopped to be “hard-linked” to Nasdaq systems. To what extent this increase in order flow fragmentation affected market functioning? Are orders executed at the best available prices on the market? We find no evidence that market quality worsened following this exit. Effective and realized spreads remained unchanged. This suggests that information dissemination and third-parties smart routing services has been sufficient to counterbalance the lack of built-in linkages. Additionally, we observed a persistent frequency of trade-through of around 15%, testifying of a non-negligible proportion of orders executed at a price worse than the best available one. However, using simulations, we showed that even when Island quote is better than the actual transaction price, an investor trading in Nasdaq would have generally experienced losses if the order were rerouted to Island. This suggests that trade-through regulation should consider depth as a major dimension.

## Order Aggressiveness and Order Book Dynamics

Anthony D. Hall, Nikolaus Hautsch
In this paper, we study the determinants of order aggressiveness and traders' order submission strategy in an open limit order book market. Using order book data from the Australian Stock Exchange, we model traders' aggressiveness in market trading, limit order trading as well as in order cancellations on both sides of the market using a six-dimensional autoregressive intensity model. The information revealed by the open order book plays an important role in explaining the degree of order aggressiveness in the individual processes. Moreover, evidence for significant dynamic interdependencies between the individual processes confirms the usefulness of the multivariate setting. Overall, our empirical results confirm theoretical findings on limit order book trading and show that a trader's decision of when and which order to submit is significantly influenced by the queued volume, the market depth, the inside spread, recent volatility, as well as recent changes in both the order flow and the price.

## Who Benefits from an Open Limit-Order Book?

Shmuel Baruch
The NYSE opened the limit-order book to off-exchange traders during trading hours. We address the welfare implications of this change in market structure. We model a market similar to the auction that the exchange uses to open the trading day. We consider two different environments. In the first, only the specialist sees the limit-order book, while in the second the information in the book is available to all traders. We compare equilibria and find that traders who demand liquidity are better off when the book is open while liquidity suppliers are better off when the book is closed.

## The Dynamics of Security Trades, Quote Revisions, and Market Depths for Actively Traded Stocks

Shafiqur Rahman, Chandrasekhar Krishnamurti and Alice C. Lee
We examine the dynamics of return volatility, trading volume, and depth—in an intraday setting for a sample of actively traded NYSE and NASDAQ stocks. We show that depth is a useful intervening variable and mitigates the impact of trading activity on price volatility. Furthermore, depth is affected by the perception of prevailing information asymmetry between informed and uninformed traders. We demonstrate empirically that the NYSE supplies greater depth under conditions of high, perceived information asymmetry as compared to NASDAQ. NASDAQ makes up for this deficiency by its capability of managing large volume shocks without a major decline in depth.

## Understanding limit order book depth: conditioning on trade informativeness

Helena Beltran, Albert J. Menkveld
We study how a limit order book reacts to informed trades and adverse selection. We estimate Sandas'(2001) version of the classical Glosten (1994) order book model and accept it, but only for the first two prices displayed on each side of the book. We then relax one of the assumption and allow the level of private information in market orders to be stochastic. By conditioning on the information level, we find support for deeper order books, larger market orders and shorter inter-trade durations at times of relatively uninformative market orders, which is consistent with liquidity traders concentrating their orders at uninformative times.

## Exclusion particle models of limit order financial markets

Damien Challet, Robin Stinchcombe
Using simple particle models of limit order markets, we argue that mid-term over-diffusive price behaviour is inherent to the very nature of these markets. Several rules for rate changes are considered. We obtain analytical results for bid-ask spread properties, Hurst plots and price increment correlation functions.

## Short-term market reaction after extreme price changes of liquid stocks

In our empirical study, we examine the price of liquid stocks after experiencing a large intraday price change using data from the NYSE and the NASDAQ. We find significant reversal for both intraday price decreases and increases. The results are stable against varying parameters. While on the NYSE the large widening of the bid-ask spread eliminates most of the profits that can be achieved by a contrarian strategy, on the NASDAQ the bid-ask spread stays almost constant yielding significant short-term abnormal profits. Furthermore, volatility, volume, and in case of the NYSE the bid-ask spread, which increase sharply at the event, decay according to a power-law and stay significantly high over days afterwards.

## Cancellation and Uncertainty Aversion on Limit Order Books

Jeremy Houston Large
This paper models limit order books where each trader is uncertain of the underlying distribution in the asset's value to others. If this uncertainty is rapidly resolved, eeting limit orders are submitted and quickly cancelled. This enhances liquidity supply, but leaves intact established comparative statics results on spreads. However, risk neutral liquidity suppliers are averse to persistent uncertainty due to concavity in the function describing limit order utility, and spreads widen. This helps explain wide spreads in the morning. The model describes traders who in equilibrium correctly anticipate market orders' endogenous stochastic intensities. It highlights how limit orders queue for execution.

## Electronic Market Making: Initial Investigation

Yuriy Nevmyvaka, Katia Sycara, Duane J. Seppi
This paper establishes an analytical foundation for electronic market making. Creating an automated securities dealer is a challenging task with important theoretical and practical implications. Our main interest is a normative automation of the market maker’s activities, as opposed to explanatory modeling of human traders, which was the primary concern of earlier work in this domain. We use a simple class of “non-predictive” trading strategies to highlight the fundamental issues. These strategies have a theoretical foundation behind them and serve as a showcase for the decisions to be addressed: depth of quote, quote positioning, timing of updates, inventory management, and others. We examine the impact of various parameters on the market maker’s performance. Although we conclude that such elementary strategies do not solve the problem completely, we are able to identify the areas that need to be addressed with more advanced tools. We hope that this paper can serve as a first step in rigorous examination of the dealer’s activities, and will be useful in disciplines outside of Finance, such as Agents, Robotics, and E-Commerce.

## Fluctuations and response in financial markets: the subtle nature of 'random' price changes

Jean-Philippe Bouchaud, Yuval Gefen, Marc Potters, Matthieu Wyart
Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to super-diffusion (or persistence), and mean reverting limit orders that lead to sub-diffusion (or anti-persistence). We define and study a model where the price, at any instant, is the result of the impact of all past trades, mediated by a non constant propagator' in time that describes the response of the market to a single trade. Within this model, the market is shown to be, in a precise sense, at a critical point, where the price is purely diffusive and the average response function almost constant. We find empirically, and discuss theoretically, a fluctuation-response relation. We also discuss the fraction of truly informed market orders, that correctly anticipate short term moves, and find that it is quite small.

## A quantitative model of trading and price formation in financial markets

Marcus G. Daniels, J. Doyne Farmer, Laszlo Gillemot, Giulia Iori, Eric Smith
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

## More statistical properties of order books and price impact

Marc Potters, Jean-Philippe Bouchaud
We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time of a limit order as a function of the distance from the best price. We also determine the price impact' function using French and British stocks, and find a logarithmic, rather than a power-law, dependence of the price response on the volume. The weak time dependence of the response function shows that the impact is, surprisingly, quasi-permanent, and suggests that trading itself is interpreted by the market as new information.

## Statistical properties of stock order books: empirical results and models

J.-P. Bouchaud, M. Mezard, M. Potters
We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of incoming limit order prices, which follows a power-law around the current price with a diverging mean; and (ii) the humped shape of the average order book, which can be quantitatively reproduced using a zero intelligence' numerical model, and qualitatively predicted using a simple approximation.

## The power of patience: A behavioral regularity in limit order placement

Ilija I. Zovko, J. Doyne Farmer
In this paper we demonstrate a striking regularity in the way people place limit orders in financial markets, using a data set consisting of roughly seven million orders from the London Stock Exchange. We define the relative limit price as the difference between the limit price and the best price available. Merging the data from 50 stocks, we demonstrate that for both buy and sell orders, the unconditional cumulative distribution of relative limit prices decays roughly as a power law with exponent approximately 1.5. This behavior spans more than two decades, ranging from a few ticks to about 2000 ticks. Time series of relative limit prices show interesting temporal structure, characterized by an autocorrelation function that asymptotically decays as tau^(-0.4). Furthermore, relative limit price levels are positively correlated with and are led by price volatility. This feedback may potentially contribute to clustered volatility.

## Econometric Analysis of Financial Transaction Data: Pitfalls and Opportunities

Nikolaus Hautsch, Winfried Pohlmeier
The recent availability of large data sets covering single transactions on financial markets has created a new branch of econometrics which has opened up a new door of looking at the microstructure of financial markets and its dynamics. The specific nature of transaction data such as the randomness of arrival times of trades, the discreteness of price jumps and significant intraday seasonalities, call for specific econometric tools combining both time series techniques as well as microeconomtric techniques arising from discrete choice analysis. This paper serves as an introduction to the econometrics of transaction data. We survey the state of the art and discuss its pitfalls and opportunities. Special emphasis is given to the analysis of the properties of data from various assets and trading mechanisms. We show that some characteristics of the transaction price process such as the dynamics of intertrade durations are quite similar across various assets with different liquidity and regardless whether an asset is traded electronically or on the floor. However, the analysis of other characteristics of transaction prices process such as volatility requires a careful choice of the appropriate econometric tool. Empirical evidence is presented using examples from stocks traded electronically and on the floor at the German Stock exchange and from BUND future trading at the LIFFE and the EUREX.

## Price fluctuations from the order book perspective - empirical facts and a simple model

Sergei Maslov, Mark Mills
Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit order sizes was found to be consistent with a power law with an exponent close to 2. A somewhat better fit to this distribution was obtained by using a log-normal distribution with an effective power law exponent equal to 2 in the middle of the observed range. The depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non-linear function of its size. A large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a short term deterministic price change, which is in accord with the law of supply and demand.