Bayes Factors for Stochastic Volatility Modeling

Eric Jacquier
Carroll School of Management, Boston College

Nicholas G. Polson
The University of Chicago

We provide a simulation based approach for model comparison in stochastic volatility models. We provide a test for the leverage effect of Black. We also provide a test for fat-tails and an omnibus test for the leverage effect in the presence of fat-tails. Our approach is based on using the output of a MCMC simulation and calculating odds ratios for competing models. It can be used for non-nested models as long as there is an underlying latent variable structure to be exploited as for stochastic volatility models. We illustrate our methodology by comparing four competing stochastic volatility models: the standard SV model; a leverage effect (SVL); SV with fat-tailed errors (SVF) and both fat-tails and leverage (SVFL). We use these odds ratios to formal test for the leverage and fat-tailed effects in a number of financial applications including returns on individual stocks; market-based indices and exchange rates. For equity returns we find overwhelming evidence for fat-tails. We find little evidence of the leverage effect for individual equity but a strong effect for market-based indices. This contradicts the financial leverage hypothese For exchange rates we generally find strong evidence of fat-tails and sometimes evidence of a leverage effect.