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.
 Spring '10
 DURRETT
 The Land

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