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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.
 Spring '13

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