A semi-Markov model for price returns

TL;DR

This paper models high-frequency stock return dynamics using a semi-Markov process for intraday returns and a Markov chain for overnight returns, deriving key statistical properties and validating with real Italian stock data.

Contribution

It introduces a semi-Markov model for high-frequency stock returns, providing new equations for first passage times and autocorrelation, and validates the model with empirical data.

Findings

Semi-Markov model accurately describes intraday return dynamics.

Derived equations match empirical first passage time distributions.

Model passes nonparametric hypothesis tests on real data.

Abstract

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday return are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorreletion function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.