A semi-Markov model with memory for price changes

TL;DR

This paper introduces a semi-Markov model with memory to analyze high-frequency stock price changes, capturing volatility regimes and aligning theoretical results with real Italian market data.

Contribution

It develops a semi-Markov model incorporating memory effects to better represent intraday price dynamics and volatility regimes.

Findings

Model accurately captures volatility periods.

Theoretical results align with empirical data.

Provides a new framework for high-frequency market analysis.

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 returns are described by a discrete time homogeneous semi-Markov which depends also on a memory index. The index is introduced to take into account periods of high and low volatility in the market. First of all we derive the equations governing the process and then 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.