General Semi-Markov Model for Limit Order Books: Theory, Implementation and Numerics

TL;DR

This paper develops a comprehensive semi-Markov model for Limit Order Books that captures complex price change dynamics, providing theoretical foundations, implementation details, and numerical validation on multiple major stock datasets.

Contribution

It introduces a generalized semi-Markov model with multiple states for price changes, extending previous models and offering a flexible framework for LOB analysis.

Findings

Model accurately captures non-fixed tick price changes.

Diffusion limits are derived for the proposed models.

Numerical results validate the model on real market data.

Abstract

The paper considers a general semi-Markov model for Limit Order Books with two states, which incorporates price changes that are not fixed to one tick. Furthermore, we introduce an even more general case of the semi-Markov model for LimitOrder Books that incorporates an arbitrary number of states for the price changes. For both cases the justifications, diffusion limits, implementations and numerical results are presented for different Limit Order Book data: Apple, Amazon, Google, Microsoft, Intel on 2012/06/21 and Cisco, Facebook, Intel, Liberty Global, Liberty Interactive, Microsoft, Vodafone from 2014/11/03 to 2014/11/07.