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Sequential Monte Carlo-ABC Methods for Estimation of Stochastic Simulation Models of the Limit Order Book

Authored by: Gareth W. Peters , Efstathios Panayi , Francois Septier

Handbook of Approximate Bayesian Computation

Print publication date:  August  2018
Online publication date:  August  2018

Print ISBN: 9781439881507
eBook ISBN: 9781315117195
Adobe ISBN:

10.1201/9781315117195-15

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Abstract

In this chapter, we consider 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). The LOB is the primary data structure recorded each day intra-daily for the majority of assets on electronic exchanges around 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 characterise 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 recently proposed by Panayi and Peters (2015), 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. One can consider this class of problems as truly a setting in which both the likelihood is intractable to evaluate pointwise, but trivial to simulate, and in addition the amount of data is massive. This is a true example of big-data application, as for each day and for each asset one can have anywhere between 100,000–500,000 data vectors for the calibration of the models.

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