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

The realized stochastic volatility model of Takahashi, Omori, and Watanabe (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is extended by employing a wider class distribution, the generalized hyperbolic skew Student's t-distribution, for nancial returns. The extension makes it possible to consider the heavy tail and skewness in 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 several backtesting procedures. Empirical results with the US index, Dow Jones Industrial Average, show that the extended model ts the data better and improves the volatility and quantile forecasts.