| Summary: | 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.
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