A Class of Stochastic Volatility Models with Copula Dependencies

Abstract

Stochastic Volatility (SV) models are a popular class of models to analyze the dependency structure between stocks and their volatility. We develop a new class of SV models by incorporating carefully selected copula structures to reconstruct stylised empirical behaviours that cannot be captured by symmetric Gaussian innovations. To estimate model parameter for each copula setting, modern Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods are applied. We use batch as well as sequential Bayesian model selection to provide insights into the suitability of different copula choices on the US equity S&P 500 and an associated volatility index. Our results provide strong evidence against the common choice of Gaussian innovations for typical SV models proposed in the financial modelling literature.