MCMC Methods for Estimating Stochastic Volatility Models with Liverage Effects: Comments on Jacquier, Polson and Rossi (2002)

Abstract

In this note we represent the well known discrete time stochastic volatility (SV) model with a leverage effect and the SV model of Jacquier, Polson and Rossi (JPR) (2002) using Gaussian nonlinear state space forms with uncorrelated measurement and transition errors. With the new representations, we show that the JPR specification does not necessarily lead to a leverage effect and hence is not theoretically justified. Empirical comparisons of these two models via Bayesian MCMC methods reveal that JPR's specification is not supported by actual data either. Simulation experiments are conducted to study the sampling properties of the Bayes estimator for the conventionally specified model.