Stochastic

# Starting at the right edge s3 ht t 2 but the maximum

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Unformatted text preview: er to sell this for \$6.50. You are delighted when a customer purchases 10,000 calls for \$65,000, but then become worried about the fact that if the stock goes up you will lose \$85,000. By (6.7) the hedge ratio 15 = 1/2 0= 30 so you borrow \$300,000 - \$65,000 = \$235,000 and buy 5,000 shares of stock. Case 1. The stock goes up to \$80. Your stock is worth \$400,000. You have to pay \$150,000 for the calls and (19/18)\$235,000 = \$248,055 to redeem the loan so you make \$1,945 (in time 1 dollars). Case 2. The stock drops to \$50. Your stock is worth \$250,000. You owe nothing for the calls but have to pay \$248,055 to redeem the loan so again you make \$1,945. The equality of the proﬁts in the two cases may look like a miracle but it is not. By buying the correct amount of stock you replicated the option. This means you made a sure proﬁt of the \$1,842 di↵erence (in time 0 dollars) between the selling price and fair price of the option, which translates into \$1,945 time 1 dollars. N period model To solve the problem in general we work backwards from the end, repeatedly applying t...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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