Problem
For these next problems use the GAIL software and consider a stock with an initial price of $30, an interest rate of 1%, and a volatility of 40%, being monitored weekly for 6 weeks.
1. What is the price of an Asian arithmetic mean call option to the nearest $0.1 if the strike price is $30?
2. What savings in number of paths and time do you find, if any, if you use a European call option as a control variate?
3. What savings in number of paths and time do you find, if any, if you use antithetic variates?