Rama Cont, Sasha Stoikov, Rishi Talreja
IEOR Dept, Columbia University, New York

We propose a stochastic model for the continuous-time dynamics of a limit order book. The model strikes
a balance between three desirable features: it can be estimated easily from data, 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. Using high-frequency data, we show that our model can effectively capture the short-term
dynamics of a limit order book. We also evaluate the performance of a simple trading strategy that is based