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Consider the stock price model in Example 13.5. The T-contract X to be priced is defined by
where a and b are given positive numbers. Thus, up to the scaling factors a and b, we obtain the maximum of the two stock prices at time T. Use Proposition 13.4 and the Black-Scholes formula in order to derive a pricing formula for this contract. See Johnson (1987).
Assume that the contract function is homogeneous of degree 1, and that the volatility matrix a is constant. Then the pricing function F is given by