There is a common options strategy, where in an investor buys the asset, buys an out-of-the-money put option on the asset, and sells an out-of-the-money call option on the asset (with the two options having the same time of expiration). Suppose John wishes to engage in such a strategy on East Coast Timber Inc, a non-dividend paying common stock, using six-month options. He would like the put to have a strike price of $45 and the call to have a strike price of $75. The current price of East Coast Timbers stock is $60 per share. Assume that John can borrow and lend at continuously compounded risk-rate of 7% per annum, and the annual variance of East Coast Timbers continuously compounded returns is 50%. Assume that the above strategy involves European-style options (i.e. option can be exercised only at end of six months)

1. a) Use the Black-Scholes model to calculate the total cost of the above strategy that John is interested in buying.

2. b) Draw the payoffs at maturity to John.

3. c) What is the maximum profit and the maximum loss that John faces?

4. d) When would John, or any other investor, be interested in such a position?