Stochastic

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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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