Title: Realized stochastic volatility models with skew-$t$ distributions
Authors: Makoto Takahashi - Hosei University (Japan) [presenting]
Yasuhiro Omori - University of Tokyo (Japan)
Toshiaki Watanabe - Hitotsubashi University (Japan)
Abstract: Predicting volatility and quantiles of financial returns is essential to measure the financial tail risk such as value-at-risk and expected shortfall. There are two important aspects of volatility and quantile forecasts: the distribution of financial returns and the estimation of the volatility. Building on the traditional stochastic volatility model, the realized stochastic volatility model incorporates the realized volatility as the precise estimator of the volatility. Using the generalized hyperbolic skew-$t$ and Azzalini skew-$t$ distributions, the model is extended to capture the well-known characteristics of the return distribution, namely skewness and heavy tails. In addition to the normal and Student's $t$ distributions included as the special cases of both distributions, the Azzalini skew-$t$ contains the skew-normal, and hence allows flexible modeling of the return distribution. The Bayesian estimation scheme via a Markov chain Monte Carlo method is developed and applied to the US and Japanese stock indices, Dow Jones Industrial Average and Nikkei 225. The estimation results show that the negative skewness is evident for both indices whereas the heavy tail is largely captured by the realized stochastic volatility, and thus demonstrate that the model with the skew-normal distribution performs well. In addition, the prediction results with a range of tests and performance measures evaluating the volatility and quantile forecasts will be presented.