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How markets slowly digest changes in supply and demand
, 2008
"... In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is ..."
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Cited by 81 (11 self)
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In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent longmemory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bidask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from
2008: Highfrequency trading in a limit order book
 Quantitative Finance
"... We study a stock dealer’s strategy for submitting bid and ask quotes in a limit order book. The agent faces an inventory risk due to the diffusive nature of the stock’s midprice and a transactions risk due to a Poisson arrival of market buy and sell orders. After setting up the agent’s problem in a ..."
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Cited by 31 (0 self)
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We study a stock dealer’s strategy for submitting bid and ask quotes in a limit order book. The agent faces an inventory risk due to the diffusive nature of the stock’s midprice and a transactions risk due to a Poisson arrival of market buy and sell orders. After setting up the agent’s problem in a maximal expected utility framework, we derive the solution in a two step procedure. First, the dealer computes a personal indifference valuation for the stock, given his current inventory. Second, he calibrates his bid and ask quotes to the market’s limit order book. We compare this ”inventorybased ” strategy to a ”naive ” strategy that is symmetric around the midprice, by simulating stock price paths and displaying the P&L profiles of both strategies. We find that our strategy yields P&L profiles and final inventories that have significantly less variance than the benchmark strategy. 1
Relation between bidask spread, impact and volatility in double auction markets
, 2006
"... We show that the cost of market orders and the profit of infinitesimal marketmaking ortaking strategies can be expressed in terms of directly observable quantities, namely the spread and the lagdependent impact function. Imposing that any market taking or liquidity providing strategies is at best ..."
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Cited by 29 (2 self)
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We show that the cost of market orders and the profit of infinitesimal marketmaking ortaking strategies can be expressed in terms of directly observable quantities, namely the spread and the lagdependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bidask 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 2 s exceeding 0.9. This correlation suggests both that the main determinant of the bidask spread is adverse selection, and that most of the volatility comes from trade impact. We argue that the role of the timehorizon appearing in the definition of costs is crucial and that longrange correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find
The Virtues and Vices of Equilibrium and the future of financial economics
, 2009
"... The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we p ..."
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Cited by 24 (1 self)
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The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, and should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out,i.e.,where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models.We sketch some alternative approaches and discuss why they should play an important role in
Price Dynamics in a Markovian Limit Order Market
 SIAM Journal for Financial Mathematics
"... We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions ..."
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Cited by 18 (0 self)
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We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in orderdriven markets. Key words: limit order book, market microstructure, queueing, diffusion limit, highfrequency data, liquidity, duration analysis, point process.
A mathematical approach to order book modeling
 International Journal of Theoretical and Applied Finance
, 2013
"... Abstract. Motivated by the desire to bridge the gap between the microscopic description of price formation (agentbased modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order b ..."
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Cited by 18 (2 self)
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Abstract. Motivated by the desire to bridge the gap between the microscopic description of price formation (agentbased modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuoustime Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaledcentered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data.
Fundamentalists Clashing over the Book: A Study of OrderDriven Stock Markets ∗
"... Abstract. Agentbased models of market dynamics must strike a compromise between the structural assumptions that represent the trading mechanism and the behavioral assumptions that describe the rules by which traders take their decisions. We present a structurally detailed model of an orderdriven st ..."
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Cited by 11 (1 self)
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Abstract. Agentbased models of market dynamics must strike a compromise between the structural assumptions that represent the trading mechanism and the behavioral assumptions that describe the rules by which traders take their decisions. We present a structurally detailed model of an orderdriven stock market and show that a minimal set of behavioral assumptions suffices to generate a leptokurtic distribution of shortterm logreturns. This result backs up the conjecture that the emergence of some statistical properties of financial time series is due to the microstructure of stock markets.
HAWKES MODEL FOR PRICE AND TRADES HIGHFREQUENCY DYNAMICS
"... Abstract. We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival selfexcitation, the ..."
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Cited by 10 (0 self)
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Abstract. We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival selfexcitation, the price changes mean reversion the impact of trade arrivals on price variations and the feedback of price changes on trading activity. It allows one to account for both stylized facts of market prices microstructure (including random time arrival of price moves, discrete price grid, high frequency mean reversion, correlation functions behavior at various time scales) and the stylized facts of market impact (mainly the concavesquarerootlike/relaxation characteristic shape of the market impact of a metaorder). Moreover, it allows one to estimate the entire market impact profile from anonymous market data. We show that these kernels can be empirically estimated from the empirical conditional mean intensities. We provide numerical examples, application to real data and comparisons to former approaches.
High frequency asymptotics for the limit order book. Preprint available on the authors’ webpage
"... We study the onesided limit order book corresponding to limit sell orders and model it as a measurevalued process. Limit orders arrive to the book according to a Poisson process and are placed on the book according to a distribution which varies depending on the current best price. Market orders t ..."
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Cited by 8 (2 self)
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We study the onesided limit order book corresponding to limit sell orders and model it as a measurevalued process. Limit orders arrive to the book according to a Poisson process and are placed on the book according to a distribution which varies depending on the current best price. Market orders to buy periodically arrive to the book according to a second, independent Poisson process and remove from the book the order corresponding to the current best price. We consider the above described limit order book in a high frequency regime in which the rate of incoming limit and market orders is large and traders place their limit sell orders close to the current best price. Our first set of results provide weak limits for the unscaled price process and the properly scaled measurevalued limit order book process in the high frequency regime. In particular, we characterize the limiting measurevalued limit order book process as the solution to a measurevalued stochastic differential equation. We then provide an analysis of both the transient and longrun behavior of the limiting limit order book process. 1