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Consider two indexes Xt, Yt that follow the processes dXt = X dt + X...

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Finance

Consider two indexes Xt, Yt that follow the processes dXt = X dt + X dWX t , dYt = Y dt + Y dWY t , where X, Y and X, Y are constants, WX t , WY t are two standard Brownian motions that satisfy dWX t dWY t = dt. Let F(Xt, Yt, t) denote the timet of another option whose payoff depends on both index, i.e.,

F(XT , YT , T) = YT if XT /2 YT < 0 and = XT if XT /2 YT 0

Use delta-hedging method to derive the Black-Schole PDE for the options value F(Xt, Yt, t).

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