Question
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
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)
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a) Use the Black-Scholes model to calculate the total cost of the above strategy that John is interested in buying.
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b) Draw the payoffs at maturity to John.
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c) What is the maximum profit and the maximum loss that John faces?
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d) When would John, or any other investor, be interested in such a position?
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