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Homework Set 2 (Spring2017).pdf

Homework Set 2 (Spring2017).pdf - Homework Set 2 STAT...

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Homework Set 2 STAT GU4265 & GR5265 – Stochastic Methods in Finance Irene Hueter 1. Consider a one-step binomial model for two no-arbitrage assets X and Y with parameters 0 < d < 1 < u, and initial price X Y (0) = 1 . We cannot assume that the dollar prices of X and Y are correlated. (a) Find the price and the hedge of a contract V that pays off V 1 = max( X 1 , Y 1 ) . (b) Compute the price of the contract V using both martingale measures P Y and P X . ( Hint : In the case that there is no perfect hedge for this model, find the hedging portfolio that minimizes the variance of the difference between the value of the contract and the value of the hedging portfolio.) 2. Consider an American contract V that pays off max(6$ τ , S τ ) = max(6 , S $ ) · $ τ at exercise time τ 2 in a two-step binomial model with parameters u = 2 , d = 1 2 , r = 1 4 , and S $ = 4
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