  Forecasting volatility and quantiles of financial returns is essential for
accurately measuring financial tail risks, such as value-at-risk and expected
shortfall. The critical elements in these forecasts involve understanding the
distribution of financial returns and accurately estimating volatility. This
paper introduces an advancement to the traditional stochastic volatility model,
termed the realized stochastic volatility model, which integrates realized
volatility as a precise estimator of volatility. To capture the well-known
characteristics of return distribution, namely skewness and heavy tails, we
incorporate three types of skew-t distributions. Among these, two distributions
include the skew-normal feature, offering enhanced flexibility in modeling the
return distribution. We employ a Bayesian estimation approach using the Markov
chain Monte Carlo method and apply it to major stock indices. Our empirical
analysis, utilizing data from US and Japanese stock indices, indicates that the
inclusion of both skewness and heavy tails in daily returns significantly
improves the accuracy of volatility and quantile forecasts.
