The data for this question is in the sheet called FinancialCalls and it contains call prices for options on BAC, GS, JPM, and MS on September 10 2008 as calibrated using an arbitrage free model with spot prices set to 100; zero rates and dividend yields, with strikes ranging in two dollar intervals from 50 to 150 for the two maturities of one and three months respectively.
(a) Graph the risk neutral densities for the four stocks at both maturities.
(b) For a continuously compounded interest rate of 3.5% per annum, determine the spot price of the contract that pays the difference between squared return at three months and the squared return at one month times a notional of 10 million dollars on each of the four underliers.
(c) Determine the optimal position in stocks and options in GS for a risk averse investor with exponential utility with absolute risk aversion coefficient 0.5 and log normal beliefs for a mean rate of return of 7% and a volatility of 15%. The utility function in this case is
u(c) = 1 - exp(-c/2)
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