Consider two correlated Ito processes X and Y that take the form X(t) dx(0 = up(t) dt + ox(t)dZ(t) dY(t) Y(t) != My(t) dt + or(t)dW(t) where Z and W are two standard Brownian processes with correlation p so that, in addition to the usual Ito expressions for (dX)2 and (dY)2 , we also have dZdW = pdt For a twice continuously differentiable functions f(t, x, y) Ito's Lemma for a function of two Brownian processes takes the form df ( t, X, n) = of at + fax + of dy + 10's at ax ay 20x 2 2av2 -dXdy axdy Show that the process G(t) = X(t) Y(t) is a geometric Brownian motion, and find the drift u and the volatility o of the motion. . You can use the box rule X dWi dt dWk Pik dt 0 dt 0 0 to compute the drift and variance of a combination of two standard Wiener processes in a sum, and take for granted that the sum of 2 Wiener processes is also a Wiener process