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

Takahashi, Makoto, Toshiaki Watanabe and Yasuhiro Omori

The realized stochastic volatility model of Takahashi, Omori, and Watanabe (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is extended with more general form of bias correction in realized volatility and wider class distribution, the generalized hyperbolic skew Student's t-distribution, for nancial returns. The extensions make it possible to adjust the bias due to the market microstructure noise and non-trading hours, which possibly depends on the level of the volatility, and 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 SPDR, the S&P 500 exchange-traded fund, show that the heavy tail and skewness of daily returns are important for the model fit and the quantile forecasts but not for the volatility forecasts, and that the additional bias correction improves the quantile forecasts but does not substantially improve the model fit nor the volatility forecasts.