The global economy has been profoundly affected by two recent crises: the Covid-19 pandemic and the Russia-Ukraine War. These events have also driven market volatility in both West Texas Intermediate (WTI) crude oil and the S&P 500 Index. The objective of this study is to analyze the market volatility of WTI crude oil and the S&P 500 Index in the context of the two aformentioned crises. Through the implementation of randomness tests and an ARCH effect test, it has been determined that ARMA-GARCH models could be useful for modeling the data in each period. Additionally, the GARCH models have been expanded to asymmetric GJR models, which account for the leverage effect. The Box-Jenkins methodology has been employed to identify the best-fitted model. The analysis reveals that WTI crude oil is more strongly impacted by the two events compared to the S&P 500 Index, suggesting that the latter is relatively less volatile. Furthermore, forecast evaluation is conducted by comparing the predicted values obtained from the best-fitted and second-best-fitted models to assess forecast accuracy. Lastly, risk determination is performed by calculating the value at risk. Based on the calculations, it is apparent that WTI crude oil carries greater risk than the S&P 500 Index during major crises. Overall, market volatility analysis provides valuable insights into the statistical behavior of different markets, enabling market participants to evaluate market risk and enhance their risk management strategies.