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)
Yuta Yamauchi - University of Tokyo (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 realized volatility as the precise estimator of the volatility. Using three types of 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 the skew-$t$ distributions, two of them contain the skew-normal, and hence allows more flexible modeling of the return distribution. The Bayesian estimation scheme via a Markov chain Monte Carlo method is developed and applied to major stock indices. 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. On the other hand, the prediction results suggest that incorporating both skewness and heavy tail to daily returns is important for volatility and quantile forecasts, especially in a high-volatility period.