1 suppose the stock price goes up to 75 in period 1

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Unformatted text preview: tively. We derive current value of the call by working backwards: first compute its value next period, and then its current value. European vs. American We can also consider through the tree whether we could exercise early or not if the option is American. Example (continued) Step 1: Start with Period 1. 1 Suppose the stock price goes up to $75 in period 1: Construct the replicating portfolio at node (t = 1, up): 112.5a + 1.1b = 62.5 37.5a + 1.1b = 0. The unique solution is a = 0.833 and b = −28.4. The cost of this portfolio is (0.833)(75) − 28.4 = 34.075. Thus, Cu = 34.075. Early Exercise Notice that 75 − 50 = 25 < 34.075. So if we exercise now we get $25 which is less than the continuation value of $34.075. So don’t exercise early for American options Put differently, if we want money now rather than exercise Keep the option Sell the replicating portfolio to get $34.075 now In the future, the payoff of the option is what we owe on the replicating portfolio that we sold so there are no net cash...
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This document was uploaded on 10/28/2013.

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