A delta-normal approach, the historical simulation approach and the monte carlo simulation approach.

Please perform empirical studies on a selected stock index (choosing the stock index by yourself) using any two of the above three approaches. Evaluate which approach is more accurate in out-of-sample value-at-risk forecasting. The conclusions should be based on your backtesting results.

Suppose for each day you invest $10million in the stock index. The daily value-at-risk is calculated at the following confidence levels: 99%, 95% and 90%. For out-of-sample value-at-risk forecasting, the time-horizon covers at least 10 years.

Please explain the VaR-method used, show the empirical results by your methods; compare the results. And write a short conclusion.