A comparison between several correlated stochastic volatility models

TL;DR

This paper compares popular stochastic volatility models like OU, Heston, and expOU by analyzing their ability to replicate market phenomena such as volatility autocorrelation and leverage effect, supported by empirical data.

Contribution

It provides a systematic comparison of SV models focusing on their limitations and empirical validation of market correlations across different indices.

Findings

Heston model best captures volatility autocorrelation

expOU model effectively reproduces leverage effect

Empirical data confirms universality of correlations

Abstract

We compare the most common SV models such as the Ornstein-Uhlenbeck (OU), the Heston and the exponential OU (expOU) models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add empirical research on market indices confirming the universality of the leverage and volatility correlations.