FBE559.slides.07

4 binomial stock example i alternate solution

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Unformatted text preview: ement is four times as big for the stock, so ∆ = 1. 4 Binomial Stock Example I: Alternate Solution (continued) Now, the portfolio of call − 1 shares of stock 4 is riskless and its final payoff is Vup = 25 − 150∆ = −12.5 Vdown = 0 − 50∆ = −12.5 So its current price must be −$12.5 discounted or: Pportfolio = (0.95)(−12.5) = −11.875 We also have: 1 Pportfolio = C0 − ∆ × S0 = C0 − 100 = C0 − 25 4 And so we must have C0 = 25 − 11.875 = 13.125. Jump to Method #1 Jump to Method #3 Are we sure this is the right price? Yes. If the price was not this value, we could buy low and sell high and make an arbitrage profit. For example, if the call cost $10 we can: 1 Buy the call (cost $10) 2 Short sell the stock (nets us $25) 3 Put $11.875 in the bank 4 Put the leftover $3.125 in our pocket There are no net cash flows in the future. Note In this case, buying the call is a good deal since it is cheap (good risk-return tradeoff). The arbitrage strategy is clearly better thou...
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This document was uploaded on 10/28/2013.

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