Consider a long position of \(\$ 1\) million on the Apple stock. To assess the risk of the position, we employ daily returns of the stock from January 2, 2001 to September 30, 2011 for 2704 observations. The daily simple returns are obtained from CRSP and in the file d-aapl-0111.txt. Let the tail probability be \(p=0.01\). Compute the VaR and ES of the position for the next trading day and the next 10 trading days using the following methods:

(a) The RiskMetrics method. Write down the fitted special \(\operatorname{IGARCH}(1,1)\) model.

(b) A Gaussian GARCH model. Write down the fitted model.

(c) A GARCH model with a standardized Student \(t\) innovations. Write down the fitted model. [You should use simulation to compute VaR and ES for the next 10 trading days based on the fitted model.]