You need to deriving an analytical formula for a European option with payoff max{S1(T)S2(T),0} where S1(T) and S2(T) are the prices of security 1 and security 2 respectively, at expiry date T. Start by considering two general tradeable securities X and Y. Define the stochastic differential equations (SDEs) for the two security price processes, {X(t)} and {Y(t)}, under the risk-neutral measure, Q, as dX(t)=(rqX)X(t)dt+XX(t)dW1Q(t)dY(t)=(rqY)Y(t)dt+YY(t)dW2Q(t) - r is the continuously compounded risk-free rate; - qX and qY denote the continuously compounded dividend yields of X and Y; - X and Y denote the volatilities of X and Y; - W1Q(t) and W2Q(t) are SBMs under Q with COV(dW1Q(t),dW2Q(t))=dt, where denotes the instantaneous correlation between the Brownian motion processes. There exists a probability measure P, such that dX(t)=(rqX+XY)X(t)dt+XX(t)dW1(t)dY(t)=(rqY+Y2)Y(t)dt+YY(t)dW2(t) where W1(t) and W2(t) are SBMs under P with COV(dW1(t),dW2(t))=dt (a) Briefly explain why the standard Brownian motion as in equation (3) can be re-expressed as dW1(t)=(dW2(t)+12dW3(t)) where W3(t) is a SBM independent of W2(t)