  This paper aims to more effectively manage and mitigate stock market risks by
accurately characterizing financial market returns and volatility. We enhance
the Stochastic Volatility (SV) model by incorporating fat-tailed distributions
and leverage effects, estimating model parameters using Markov Chain Monte
Carlo (MCMC) methods. By integrating extreme value theory (EVT) to fit the tail
distribution of standard residuals, we develop the SV-EVT-VaR-based dynamic
model. Our empirical analysis, using daily S\&P 500 index data and simulated
returns, shows that SV-EVT-based models outperform others in backtesting. These
models effectively capture the fat-tailed properties of financial returns and
the leverage effect, proving superior for out-of-sample data analysis.
