The stochastic volatility model usually incorporates asymmetric effects by introducing
the negative correlation between the innovations in returns and volatility. In this paper,
we propose a new asymmetric stochastic volatility model, based on the leverage and
size effects. The model is a generalization of the exponential GARCH (EGARCH)
model of Nelson (1991). We consider categories for asymmetric effects, which
describes the difference among the asymmetric effect of the EGARCH model, the
threshold effects indicator function of Glosten, Jagannathan and Runkle (1992), and
the negative correlation between the innovations in returns and volatility. The new
model is estimated by the efficient importance sampling method of Liesenfeld and
Richard (2003), and the finite sample properties of the estimator are investigated using
numerical simulations. Four financial time series are used to estimate the alternative
asymmetric SV models, with empirical asymmetric effects found to be statistically
significant in each case. The empirical results for S&P 500 and Yen/USD returns
indicate that the leverage and size effects are significant, supporting the general model.
For TOPIX and USD/AUD returns, the size effect is insignificant, favoring the
negative correlation between the innovations in returns and volatility. We also consider
standardized t distribution for capturing the tail behavior. The results for Yen/USD
returns show that the model is correctly specified, while the results for three other data
sets suggest there is scope for improvement.
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