2015 Fall Derivatives Final.pdf

# Buying the call shorting the stock and keeping an

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buying the call, shorting the stock, and keeping an amount of cash that when invested at the risk-free rate will grow to be sufficient to exercise the call. If the stock price is above the strike price, the call is exercised and the short position is closed out for no net payoff. If the stock price is below the strike price, the call is not exercised and the short position is closed out for a gain equal to the put payoff. 9. Aristotle related a story about how the Greek philosopher Thales profited handsomely from an option-type agreement around the 6th century B.C. According to the story, one-year ahead, Thales forecast the next olive harvest would be an exceptionally good one. As a poor philosopher, he did not have many financial resources at hand. But he used what he had to place a deposit on the local olive presses. As nobody knew for certain whether the harvest would be good or bad, Thalus secured the rights to the presses at a relatively low rate. When the harvest proved to be bountiful, and so demand for the presses was high, Thalus charged a high price for their use and reaped a considerable profit. a. What kind of option did Thales purchase? b. Assume that the premium that Thales paid was 2 gold Lydian Lions. If the price of olive press at the time of the deal was 3 Gold Lydian Lions, the strike price is

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0.25 Lydian Lions, and the relevant discount rate was 10%, did Thales get an unusually good deal or not? a. Thales purchases a call option. Because he “secured the rights to the presses at a relatively low rate”, it is the same as we buy call option in order to get the right to buy a stock at a lower price at or before expiration. b. Present value of profit = @R-.BK AH-.A − 2 = 0.5 > 0 Therefore, Thales gains 0.5 gold Lydian Lions at the present value. It is a good deal.
• Fall '16
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