Unformatted text preview: t is C0 , the value of the option today?
Claim: We can form a portfolio of stock and bond that gives
identical payoﬀs as the call.
Consider a portfolio (a, b ) where
a is the number of shares of the stock held
b is the dollar amount invested in the riskless bond.
We want to ﬁnd (a, b ) so that
75a + 1.1b = 25 25a + 1.1b = 0. There is a unique solution
a = 0.5 and b = −11.36. Example (continued) That is
buy half a share of stock and sell $11.36 worth of bond
payoﬀ of this portfolio is identical to that of the call
present value of the call must equal the current cost of this
“replicating portfolio” which is
(50)(0.5) − 11.36 = 13.64. Now we generalize the above example when there are two periods
to go: period 1 and period 2. The stock price process is:
75 112.5
37.5 S =50
25 37.5
12.5 The call price follows the following process:
Cu Cuu = 62.5
Cud = 0 C
Cd Cdu = 0
Cdd = 0 the terminal value of the call is known, and
Cu and Cd denote the option value next period when the
stock price goes up and goes down, respec...
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This document was uploaded on 10/28/2013.
 Spring '13

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