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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 out-of-the-money 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 Black-Scholes 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