Homework Set 2STAT GU4265 & GR5265 – Stochastic Methods in FinanceIrene Hueter1.Consider a one-step binomial model for two no-arbitrage assetsXandYwith parameters0< d <1< u,and initial priceXY(0) = 1.We cannot assume that the dollar prices ofXandYare correlated.(a) Find the price and the hedge of a contractVthat pays offV1= max(X1, Y1).(b) Compute the price of the contractVusing both martingale measuresPYandPX.(Hint: In the case that there is no perfect hedge for this model, find the hedging portfoliothat minimizes the variance of the difference between the value of the contract and the valueof the hedging portfolio.)2.Consider an American contractVthat pays off max(6$τ, Sτ) = max(6, S$)·$τat exercisetimeτ≤2 in a two-step binomial model with parametersu= 2, d=12, r=14,andS$= 4
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