Weighted-indexed semi-Markov models for modeling financial returns

TL;DR

This paper introduces a weighted-indexed semi-Markov model to accurately simulate high-frequency stock price dynamics, capturing key stylized facts like volatility persistence and passage times.

Contribution

It generalizes semi-Markov chains to better model financial returns, validated through simulations and real market data from Italy and Germany.

Findings

Model reproduces stylized facts of financial data

Successfully applied to Italian and German stock markets

Captures volatility persistence and passage time distributions

Abstract

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010.