Consider the daily returns of GE stock from July 3, 1962 to December 31, 1999. The data can be obtained from CRSP or the file d-ge6299.txt Convert the simple returns into log returns. Suppose that you hold a long position on the stock valued at $1 million. Use the tail probability 0.05.

Compute the value at risk of your position for 1-day horizon and 15-day horizon using the following methods:

(a) The RiskMetrics method.

(b) A Gaussian ARMA–GARCH model.

(c) An ARMA–GARCH model with a Student-t distribution. You should also estimate the degrees of freedom.

(d) The traditional extreme value theory with subperiod length n =

21.