Realized Stochastic Volatility Model with Skew-t Distributions for Improved Volatility and Quantile Forecasting

Abstract

Accurate forecasting of volatility and return quantiles is essential for evaluating financial tail risks such as value-at-risk and expected shortfall. This study proposes an extension of the traditional stochastic volatility model, termed the realized stochastic volatility model, that incorporates realized volatility as an efficient proxy for latent volatility. To better capture the stylized features of financial return distributions, particularly skewness and heavy tails, we introduce three variants of skewed t-distributions, two of which incorporate skew-normal components to flexibly model asymmetry. The models are estimated using a Bayesian Markov chain Monte Carlo approach and applied to daily returns and realized volatilities from major U.S. and Japanese stock indices. Empirical results demonstrate that incorporating both realized volatility and flexible return distributions substantially improves the accuracy of volatility and tail risk forecasts.