SMC-ABC methods for the estimation of stochastic simulation models of the limit order book

Abstract: In this paper we consider classes of models that have been recently developed for quantitative finance that involve modelling a highly complex multivariate, multi-attribute stochastic process known as the Limit Order Book (LOB). The LOB is the primary data structure recorded each day intra-daily for all assets on every electronic exchange in the world in which trading takes place. As such, it represents one of the most important fundamental structures to study from a stochastic process perspective if one wishes to characterize features of stochastic dynamics for price, volume, liquidity and other important attributes for a traded asset. In this paper we aim to adopt the model structure which develops a stochastic model framework for the LOB of a given asset and to explain how to perform calibration of this stochastic model to real observed LOB data for a range of different assets.