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Unformatted text preview: IEOR 4701, HMWK 5, Professor Sigman 1. A stock has an initial price of S = 40. S n denotes the price at time t = n , where we assume the binomial lattice model with parameters u = 1 . 25 d = 0 . 8 p = 0 . 60 . (a) Compute E ( S 1 45) + , the expected payoff of a European call option having expi ration date n = 1 and strike price K = 45. (b) Let M 2 = max { S ,S 1 ,S 2 } and m 2 = min { S ,S 1 ,S 2 } . Compute E ( M 2 ) and E ( m 2 ). (Hint: either the stock goes up twice, down twice, up then down or down then up: 4 possibilities only.) 2. Continuation: The interest rate is r = 0 . 05. (a) Compute p * , the riskneutral probability. (b) Compute the price of a European call option with strike price K = 45 when the expiration time is T = 1, and T = 2. (c) Lookback options: Let M 2 = max { S ,S 1 ,S 2 } and m 2 = min { S ,S 1 ,S 2 } . Compute the price of the following two options which have expiration time T = 2 with the following payoffs: C 2 = M 2 S 2 , and C 2 = S 2 m 2 ....
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This note was uploaded on 10/16/2010 for the course IEOR 4701 taught by Professor Karlsigma during the Summer '10 term at Columbia.
 Summer '10
 KarlSigma

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