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Mathematics and Financial Economics

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08-01-2019

A switching microstructure model for stock prices

Authors: Donatien Hainaut, Stephane Goutte

Published in: Mathematics and Financial Economics | Issue 3/2019

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Abstract

This article proposes a microstructure model for stock prices in which parameters are modulated by a Markov chain determining the market behaviour. In this approach, called the switching microstructure model (SMM), the stock price is the result of the balance between the supply and the demand for shares. The arrivals of bid and ask orders are represented by two mutually- and self-excited processes. The intensities of these processes converge to a mean reversion level that depends upon the regime of the Markov chain. The first part of this work studies the mathematical properties of the SMM. The second part focuses on the econometric estimation of parameters. For this purpose, we combine a particle filter with a Markov chain Monte Carlo algorithm. Finally, we calibrate the SMM with two and three regimes to daily returns of the S&P 500 and compare them with a non switching model.

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Chosen parameters are in the same range of values as real estimates reported in Sect. 4.2. In order to clearly vizualize changes of regimes, the gap between mean reversion levels in each regimes is increased. For the same reason, we have also modified transition probabilities in order to observe a sufficient number of changes of regime during the simulation.

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Title: A switching microstructure model for stock prices
Authors: Donatien Hainaut
Stephane Goutte
Publication date: 08-01-2019
Publisher: Springer Berlin Heidelberg
Published in: Mathematics and Financial Economics / Issue 3/2019
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-018-00234-6

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