A Bayesian Semiparametric Model for Volatility with a Leverage Effect

Abstract

A Bayesian semiparametric stochastic volatility model for financial data is developed. This estimates the return distribution from the data allowing for stylized facts such as heavy tails and jumps in prices whilst also allowing for correlation between the returns and changes in volatility, the leverage effect. An efficient MCMC algorithm for inference is described. The model is applied to simulated data and two real data sets. These show that parametric assumptions about the return distribution can have a substantial effect on estimation of the leverage effect.

Keywords: Dirichlet process, asset return, stock index, off-set mixture representation, mixture model, centred representation

JEL Classification: C11, C14, C22