Again, consider the position and data of Exercise 1. Answer the following questions:

(a) Obtain estimates of \(\mu, \sigma\), and \(\xi\) using the traditional EVT with subperiod length \(n=21\) and 42 , respectively.

(b) Use the estimates to compute \(\mathrm{VaR}_{0.95}\) and \(\mathrm{VaR}_{0.99}\) for the next trading day and the next 10 trading days.

Data From Exercise 1:

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: