4106-08-h6 - HMWK 6 1. A stock has an initial price of S =...

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Unformatted text preview: HMWK 6 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 . The interest rate is r = 0 . 05. (Note that ud = du = 1.) (a) Compute E ( S 1 ) and E ( S 2 ). (b) Compute p * , the risk-neutral probability. (c) Compute the price of a European call option with strike price K = 45 when the expiration time is T = 1, and for T = 2. 2. Recall the car replacement problem (Example 7.12 in Text, Page 434) using the renewal reward theorem to find the optimal value of T (the one that minimizes cost). For each T > 0, the long-run cost rate is given by g ( T ) = C 1 + C 2 H ( T ) R T H ( x ) dx , where C 1 > 0 is the cost of a new car, C 2 > 0 is the cost of breakdown, and H ( x ) = P ( V ≤ x ) is the car lifetime distribution; H ( x ) = P ( V > x ) its tail. Prove that when H is exponential, the minimum value of g ( T ) is acheived at T = ∞ ; there is no finite optimal value of...
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This note was uploaded on 10/20/2010 for the course IEOR 4106 taught by Professor Whitt during the Fall '08 term at Columbia.

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