A Stochastic Partial Differential Equation Model for Limit Order Book Dynamics

39 Pages Posted: 22 Apr 2019 Last revised: 15 Jan 2021

Date Written: April 4, 2019


We propose an analytically tractable class of models for the dynamics of a limit order book, described as the solution of a stochastic partial differential equation (SPDE) with multiplicative noise. We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient methods for estimation and computation.

We study two examples of parsimonious models in this class: a two-factor model and a model in which the order book depth is mean-reverting. For each model we perform a detailed analysis of the role of different parameters, study the dynamics of the price, order book depth, volume and order imbalance, provide an intuitive financial interpretation of the variables involved and show how the model reproduces statistical properties of price changes, market depth and order flow in limit order markets.

Keywords: limit order book, volatility, market microstructure, liquidity, intraday price dynamics

JEL Classification: C14, C45, C58, G12

Suggested Citation

Cont, Rama and Mueller, Marvin S., A Stochastic Partial Differential Equation Model for Limit Order Book Dynamics (April 4, 2019). Available at SSRN: https://ssrn.com/abstract=3366536 or http://dx.doi.org/10.2139/ssrn.3366536

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk/people/rama.cont

Marvin S. Mueller

2Xideas ( email )

Kuesnacht, Zurich

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