General asymmetric stochastic volatility models using range data: estimation and empirical evidence from emerging equity markets

Abstract

We extend the range-based approach of Alizadeh et al. (2002) in order to deal with leverage and size effects and nonnormal conditional distribution in Stochastic Volatility (SV) models. We employ the Efficient Importance Sampling (EIS) method to estimate the range-based asymmetric SV models. Empirical results for the stock market indices of the Association of Southeast Asian Nations (ASEAN5) countries show that the conditional distributions of stock returns are nonnormal and that the model considered captures the existence/absence of the leverage and size effects.

Acknowledgements

The authors wish to thank Yoshi Baba for helpful discussions and would like to acknowledge the Faculty Exchange Program of Soka University and De La Salle University, Manila for their support.

Notes

¹ Asai and McAleer (2008) discuss and estimate the general ASV model (1) and (2) using the log-variance β _t = 2α _t instead of α _t .

² See also Asai et al. (2006) for the application of the EIS technique to univariate and multivariate SV models.

³ For the nonnormal case, the mean of d_t in (3) is μ + ν, which requires a value for ν in order to estimate μ. We follow Alizadeh et al. (2002) and set ν = 0.43.

⁴ Since Jarque–Bera test for skewness is invalid when kurtosis is different from 3, we employed the method of Godfrey and Orme (1991) for the test under heavy-tailed distributions. See also Asai and Dashzeveg (2008).

⁵ Results for autocorrelations are not shown in the table in order to save space. They are available from the authors upon request.

⁶ See Selçuk (2005) for estimates of φ for emerging markets.

⁷ See Asai et al. (2006) for the Bayesian MCMC estimation of the SV models.