The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Computing Laplace Transforms for Numerical Inversion Via Continued Fractions
INFORMS Journal on Computing
Analysis of chain reaction between two stock indices fluctuations by statistical physics systems
WSEAS Transactions on Mathematics
Exact Simulation of Point Processes with Stochastic Intensities
Operations Research
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We propose a continuous-time stochastic model for the 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 simple matrix computations and 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 midprice, 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 based on our results.