Dynamic Leverage and Threshold Effects in Stochastic Volatility Models*

In this paper we examine two methods for modelling asymmetries, namely dynamic leverage and threshold effects, in Stochastic Volatility (SV) models, one based on the threshold effects (TE) indicator function of Glosten, Jagannathan and Runkle (1992), and the other on dynamic leverage (DL), or the negative correlation between the innovations in returns and volatility. A general dynamic leverage threshold effects (DLTE) SV model is also used to enable non-nested tests of the two asymmetric SV models against each other to be calculated. The three SV models are estimated by the Monte Carlo likelihood (MCL) method proposed by Sandmann and Koopman (1998), and the finite sample properties of the estimator are investigated using numerical simulations. As the numerical simulation results show that the MCL estimator is biased, a simple method for correcting the bias is suggested and the performance of the bias-corrected MCL estimators is evaluated. Four financial time series are used to estimate the SV models, with empirical asymmetric effects found to be statistically significant in each case. The empirical results for S&P 500, TOPIX and Yen/USD returns indicate that dynamic leverage dominates the threshold effects model for capturing asymmetric behaviour, while the results for USD/AUD returns show that both the non-nested dynamic leverage and threshold effects models are rejected against each other. For the four data series considered, the dynamic leverage model dominates the threshold effects model in capturing asymmetric effects. In all cases, there is significant evidence of asymmetries in the general DLTE model.