Alternative Formulations of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy-Tailed Errors

Abstract

This paper investigates three formulations of the leverage effect in a stochastic volatility model with a skewed and heavy-tailed observation distribu- tion. The first formulation is the conventional one, where the observation and evo- lution errors are correlated. The second is a hierarchical one, where log-volatility depends on the past log-return multiplied by a time-varying latent coefficient. In the third formulation, this coefficient is replaced by a constant. The three models are compared with each other and with a GARCH formulation, using Bayes fac- tors. MCMC estimation relies on a parametric proposal density estimated from the output of a particle smoother. The results, obtained with recent S&P500 and Swiss Market Index data, suggest that the last two leverage formulations strongly dominate the conventional one. The performance of the MCMC method is consis- tent across models and sample sizes, and its implementation only requires a very modest (and constant) number of filter and smoother particles.