Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution

The predictive performance of the realized stochastic volatility model of Takahashi et al. (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is investigated. Considering the well-known characteristics of financial returns, namely heavy tails and skewness, the model is extended by employing a wider class distribution, the generalized hyperbolic skew Student’s tt-distribution, for financial returns. Using the Bayesian estimation scheme via a 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 the volatility and return quantiles by sampling from their posterior distributions jointly. The model is applied to quantile forecasts of financial returns such as value-at-risk and expected shortfall, as well as to volatility forecasts, and the forecasts are evaluated using a range of tests and performance measures. The empirical results using the US and Japanese stock indices, the Dow Jones Industrial Average and Nikkei 225, show that the extended model improves the volatility and quantile forecasts, especially in some volatile periods.