ABSTRACT
This chapter considers classes of models that have been recently developed for quantitative finance that involve modelling a highly complex multi-variate, multi-attribute stochastic process known as the limit order book (LOB). It develops a LOB stochastic agent model based on liquidity provision for the class of assets operating under a continuous trading mode, which will be the case for the majority of assets traded on major indices, for example. The chapter utilises model-based summary statistics which are obtained via an application specific dimension reduction approach. It explores the notion of model-based summary statistics based around first a dimension reduction of the LOB stochastic process to a subset of important features representative of key attributes of the LOB process from the practitioners' and regulators' perspective. The chapter proposes a stochastic agent-based liquidity supply and demand-based simulation model to characterise the LOB for an asset traded on an electronic exchange.
