1b 25 25a 11b 0 there is a unique solution a

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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.

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