PS8Solutions_09

PS8Solutions_09 - Solution to Problem Set 8 Investments...

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Solution to Problem Set 8 Investments Prof. Pierre-Olivier Weill 1. The option price tree is: t = 0 t = 1 t = 2 10 9.52 6.80 10 4.76 0 This is seen as follows: (a) If the stock price is 144 or 108 at maturity, then the option is worth 10. If the stock price is 81 then the option is worthless. (b) Suppose, at time 1, the stock price is 120. Then, next year the option will be worth 10 for sure. This payoF can be replicated by saving 10/1.05=9.52 at the riskfree rate of 5%. Hence, at time 1 in the upper-branch scenario, the option value is 9.52. (c) Suppose at time 1, the stock price is 90. Then, next year the option will be worth either 10 or 0, depending on whether the stock price goes up or down. Suppose that we buy Δ stocks and short a zero-coupon bond (ZCB) with face value F . Then, if the stock price goes up, the portfolio will be worth Δ * 108 - F . If the stock price goes down, the portfolio will be worth Δ * 81 - F .
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This note was uploaded on 02/04/2010 for the course ECON 106v taught by Professor Miyakawa during the Spring '08 term at UCLA.

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PS8Solutions_09 - Solution to Problem Set 8 Investments...

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