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Homework 5

# Homework 5 - IEOR 4701 HMWK 5 Professor Sigman 1 A stock...

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IEOR 4701, HMWK 5, Professor Sigman 1. A stock has an initial price of S 0 = 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 0 , S 1 , S 2 } and m 2 = min { S 0 , 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 risk-neutral 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) Look-back options: Let M 2 = max { S 0 , S 1 , S 2 } and m 2 = min { S 0 , 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 . (d) Asian call option: Compute the price of an option with payoff at time T = 2 given by ( S (2) - 45) + , where S (2) = 1 2 ( S 1 + S 2 ) .

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