The options value next period is either 34075 or 0

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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 value. 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.

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