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Unformatted text preview: Math 623, W 2007: Homework 4. For full credit, your solutions must be clearly presented and all code included. Time is counted in years and the interest rate is r = 2%, continuously compounded. (1) In this problem you are asked to value an out-of-the-money bear spread option using Monte Carlo simulations. The option expires at T = 1 (today is t = 0) and has payoff Φ( S T ), where Φ( S ) = 10 if S ≤ 50 60- S if 50 ≤ S ≤ 60 if S ≥ 60 . the interest rate is r = 2%, continuously compounded, and the volatility of the stock is σ = 0 . 2. The stock pays no dividends and is currently trading at S = 100. (a) Write the value of the stock price S T at time T as a function of a standard normal variate ξ (under the risk-neutral measure). (b) Using the Black-Scholes formula, find the exact value of the bear spread option. (c) Use “vanilla” Monte Carlo to compute the price of the option by generating samples of the standard normal variate ξ in (a). Do not use any variance reduction techniques. Report the number of paths used (the more, the better. . . ), the final Monte Carlo estimate, the standard error, and a convergence diagram....
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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