Question: Suppose that S = 100, = 0.3, r = 8%, and = 0. Today you buy a contract which, 6 months from today, will give

Suppose that S = 100, = 0.3, r = 8%, and = 0. Today you buy a contract which, 6 months from today, will give you one 3-month to expiration at-the-money call option. This is called a forward start option. Assume that r, , and do not change. i. Six months from today, what will be the value of the option if the stock price is 100? 50? 200? (Use Black-Scholes formula.) In each case, what fraction of the stock price does the option cost? ii. What investment today would guarantee that you had the money in 6 months to buy an at-the-money call option? iii. What would you pay today for the forward start option in this example?

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