Stochastic volatility models are used to predict changes in financial market volatility over time. This study looks at different models and uses Monte Carlo simulations to compare their effectiveness. By incorporating jump components, the models better fit real data. The researchers found that using an adaptive Monte Carlo method reduced autocorrelation in the volatility process. They ranked the models using the Bayes factor, a statistical measure. Despite the complexity of the computations, the researchers were able to estimate the posterior distribution accurately. The models were also validated by forecasting Value at Risk (VaR) for the S&P 500 index.