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Unformatted text preview: AMS517 Homework 1 (Due Feb 24) 1. The file intel d logret.txt contains daily log returns of Intel stock from July 9, 1986 to June 29, 2007. Compute the 99% 1-day and 10-day VaR for a long position of $1 million using the following methods: (a) GARCH(1 , 1) model with standard normal t ; (b) ARMA(1 , 1)-GARCH(1 , 1) model with t having the standardized Student t-distribution whose degrees of freedom are to be estimated from the data; (c) the GEV distribution for extreme (negative) returns with subperiod length of 20 trading days. 2. Consider a European call option with parameters as follows: current stock price S , strike K , risk-free rate r , volatility rate σ , and time to maturity T years. Assuming a geometric Brownian motion for the stock price process S t , use the delta-normal valuation to compute the 95% VaR and ES over a horizon of 5 days for (a) a short position and (b) a long position....
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- Spring '11
- Normal Distribution, 5 days, $1 million, 10-day, 1-Day, bivariate Gaussian copula