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# Lecture%2022 - Lecture 22 I. A) Option Valuation Option...

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Lecture 22 I. Option Valuation A) Option pricing problem. Suppose I have a stock with price 50 and a risk-free bond with price 100. Next period the bond will be worth 105 (5% interest rate) The stock will be worth 70 if times are good and 30 if times are bad. Stock Price 70 50 30 There exists a call option with a strike price of 50. What should this call be worth? To answer this, form a risk-less portfolio by selling one call option and buying H shares of the stock. How do we pick H? Choose H to set the payoffs of your portfolio equal to each other in every state (after all it’s a risk-less portfolio) If stock rises your portfolio is worth 70H-20 If stock price falls your portfolio is worth 30H. 70H - 20 = 30H + 0 H = .5 (buy ½ of a share for every call you short) What is the payoff from this portfolio? If stock rises your portfolio is worth 70H-20 = (70*1/2) – 20 = 15 If stock price falls your portfolio is worth 30H = 30*1/2 = 15 Recall the risk-free bond is worth 105 next period

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## This note was uploaded on 04/12/2008 for the course ECON 435 taught by Professor Chabot during the Winter '08 term at University of Michigan.

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Lecture%2022 - Lecture 22 I. A) Option Valuation Option...

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