Alternative Asymmetric Stochastic Volatility Models

Manabu Asai · Michael J. McAleer

49 citations0/0 files storedEconometric Reviews

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Market Dynamics and Volatility

Abstract

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 Nelson , D. B. ( 1991 ). Conditional heteroskedasticity in asset returns: a new approach . Econometrica 59 : 347 – 370 .[Crossref], [Web of Science ®] , [Google Scholar]). 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 et al. (1992 Glosten , L. , Jagannathan , R. , Runkle , D. ( 1992 ). On the relation between the expected value and volatility of nominal excess returns on stocks . Journal of Finance 46 : 1779 – 1801 . [Google Scholar]), 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 stochastic volatility (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 Tokyo stock price index (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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References

1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 1992ARCH modeling in finance 1987The Pricing of Options on Assets with Stochastic Volatilities 1987Expected stock returns and volatility 1982The stochastic behavior of common stock variances Value, leverage and interest rate effects 1998Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models

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