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Unformatted text preview: Math 623, F 2011: Homework 4. For full credit, your solutions must be clearly presented and all code included. (1) In this problem we will be interested in valuing an outofthemoney bear spread option on a stock S t which evolves by geometric Brownian motion with volatility σ = 0 . 20. The risk free rate is r = 0 . 046 and the expiration date of the option is T = 0 . 8. The payoff on the option is Φ( S T ), where Φ( S ) = 10 if S ≤ 40 50 S if 40 ≤ S ≤ 50 if S ≥ 50 . The stock is currently trading (at time t = 0) at a value S . (a) Show that the bear spread option is equivalent to the difference of two put options. (b) Using the MATLAB function blsprice or alternative method of computing the BlackScholes formula, graph the value of the bear spread option as a function of S , for S in the range 50 ≤ S ≤ 80. Compute the value of the option for S = 80. (c) Use the Monte Carlo method with N = 10 5 to compute the price of the option for the same range of values of S as in part (b) and graph the value of the bear spread option as a function of S . Compare with the graph in (b). Compute the value of the option for S = 80....
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This note was uploaded on 12/08/2011 for the course MATH 623 taught by Professor Conlon during the Fall '08 term at University of Michigan.
 Fall '08
 CONLON
 Math

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