"Volatility and Quantile Forecasts by Realized Stochastic Volatility Models with Generalized Hyperbolic Distribution"

Takahashi, Makoto, Toshiaki Watanabe and Yasuhiro Omori

May 2015

The predictive performance of the realized stochastic volatility model of Takahashi,　Omori, and Watanabe (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is investigated. Considering well known characteristics of nancial returns, heavy tail and negative skewness, the model is extended by employing a wider class distribution, the generalized hyperbolic skew Student's t-distribution, for nancial returns. With the Bayesian estimation scheme via Markov chain Monte Carlo method, the model enables us to estimate the parameters in the return distribution and in the model jointly. It also makes it possible to forecast volatility and return quantiles by sampling from their posterior distributions jointly. The model　is applied to quantile forecasts of nancial returns such as value-at-risk and expected shortfall as well as volatility forecasts and those forecasts are evaluated by various tests　and performance measures. Empirical results with the US and Japanese stock indices, Dow Jones Industrial Average and Nikkei 225, show that the extended model improves　the volatility and quantile forecasts especially in some volatile periods.