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Unformatted text preview: HMWK 6 Solutions 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 riskneutral 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. i. Note that E ( Y ) = [ . 6(1 . 25) + . 4(0 . 8)] = 1 . 07. E ( S 1 ) = S E ( Y 1 ) = 40[ . 6(1 . 25) + . 4(0 . 8)] = 40(1 . 07) = 42 . 8. E ( S 2 ) = S E ( Y 1 ) E ( Y 2 ) = S [ E ( Y )] 2 = 40[1 . 07] 2 = 45 . 8. ii. p * = 1 + r d u d = 1 . 05 . 8 1 . 25 . 8 = . 556 , 1 p * = 0 . 444 iii. C = = 1 1 + r E * ( C 1 ) = 1 1 + r [( uS K ) + p * + ( dS K ) + (1 p * )] = 1 1 . 05 [(5)( . 556) + 0] = 2 . 65 . T = 2: C = = 1 (1 + r ) 2 E * ( C 2 ) = 1 (1 + r ) 2 [( u 2 S K ) + ( p * 2 ) + ( udS K ) + (2 p * (1 p * )) + ( d 2 S K ) +...
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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.
 Fall '08
 Whitt
 Operations Research

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