A2 buy one share at time 1 if the stock is at 120 and

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Unformatted text preview: to buy the stock (but not an obligation to do so) for 100 at time 1. If the stock price is 80, you will not exercise the option to purchase the stock and your profit will be 0. If the stock price is 120 you will choose to buy the stock at 100 and then immediately sell it at 120 to get a profit of 20. Combining the two cases we can write the payo↵ in general as (X1 100)+ , where z + = max{z, 0} denotes the positive part of z . Our problem is to figure out the right price for this option. At first glance this may seem impossible since we have not assigned probabilities to the various events. However, it is a miracle of “pricing by the absence of arbitrage” that in this case we do not have to assign probabilities to the events to compute the price. To explain this we start by noting that X1 will be 120 (“up”) or 80 (“down”) for a profit of 30 or a loss of 10, respectively. If we pay c for the option, then when X1 is up we make a profit of 20 c, but when it is down we make c. The last two sentences are summarized in the following tab...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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