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We propose a stochastic model for the continuous-time dynamics of a limit order book. The model strikes a balance between two desirable features: it captures key empirical properties of order book dynamics and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on high-frequency observations of the order book and illustrate the results on data from the Tokyo stock exchange. Using Laplace transform methods, we are able to eﬃciently compute probabilities of various events, conditional on the state of the order book: an increase in the mid-price, execution of an order at the bid before the ask quote moves, and execution of both a buy and a sell order at the best quotes before the price moves. Comparison with high-frequency data shows that our model can capture accurately the short term dynamics of the limit order book.

A stochastic model for order book dynamics

Rama Cont
Columbia Center for Financial Engineering; Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Sasha Stoikov
Cornell Financial Engineering Manhattan

Rishi Talreja
Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

1 Introduction

The evolution of prices in ﬁnancial markets results from the interaction of buy and sell orders through a rather complex dynamic process. Studies of the mechanisms involved in trading ﬁnancial assets have traditionally focused on quote-driven markets, where a market maker or dealer centralizes buy and sell orders and provides liquidity by setting bid and ask quotes. The NYSE specialist system is an example of this mechanism. In recent years, Electronic Communications Networks (ECN’s) such as Archipelago, Instinet, Brut and Tradebook have captured a large share of the order ﬂow by providing an alternative order-driven trading system. These electronic platforms aggregate all outstanding limit orders in a limit order book that is available to market participants and market orders are executed against the best available prices. As a result of the ECN’s popularity, established exchanges such as the NYSE, Nasdaq, the Tokyo Stock Exchange and the London Stock Exchange have adopted electronic order-driven platforms, either fully or partially through “hybrid” systems. ...

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