Stochastic Volatility Models: Conditional Normality versus Heavy-Tailed Distributions

Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal distribution is compared with SV speciications using conditional heavy-tailed distributions, especially Student's t-distribution and the generalized error distribution. To estimate the SV speciications a simulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional heavy-tailed distribution. Finally, it turns out that the choice of the conditional distribution has systematic eeects on the parameter estimates of the volatility process.