Homework Set 7STAT GU4265 & GR5265 – Stochastic Methods in FinanceIrene Hueter1.Derive the optimal choiceL*of a barrier on the stock price for a perpetual Americanput as the value ofLthat maximizes the functionh(L) = (K-L)·(xL)-2rσ2,whereKis the strike,ris the constant short rate of interest, andσis the volatility constant.Here,xis a place holder for the stock price. The assumption is that the stock price followsgeometric Brownian motion. Show all your steps of the derivation.2.-4.Solve the problems # 22.5, 22.7, 24.1 in the textbook by Bj¨
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