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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).
 Spring '10
 DURRETT
 The Land

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