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Unformatted text preview: ﬂows. Example (continued) Step 1 (continued):
2 Suppose the stock price goes down to $25 in period 1. Repeat
the above for node (t = 1, down):
The replicating portfolio is a=0 and b = 0. The call value at the lower node next period is Cd = 0. Example (continued)
Step 2: Now go back one period, to Period 0.
The option’s value next period is either 34.075 or 0 depending
upon whether the stock price goes up or down:
C0 Cu = 34.075
Cd = 0 If we can construct a portfolio of the stock and bond to
“replicate” the value of the option next period, then the cost
of this “replicating portfolio” must equal the option’s present
Find a and b so that
75a + 1.1b = 34.075 25a + 1.1b = 0. The unique solution is
a = 0.6815 and b = −15.48. Step 2: (continued)
The cost of this portfolio is
(0.6815)(50) − 15.48 = 18.59.
The present value of the option must be C0 = 18.59 (which is
greater than the exercise value 0). Note: this also conﬁrms that the option will not be exercised
before maturity. Summary of the replic...
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This document was uploaded on 10/28/2013.
- Spring '13