SDE 1 is S1 = S10 exp( (r1-sigma^2/2) * dt + sigma dW1 )
S2 = S20 exp( (r2-sigma2^2/2) * dt + sigma2 dW2 )
E[dW1 dW2] = rho
I want to price an option on S1 x S2 I know I need to use the SDE's to find the SDE for d(S1 S2) using Ito...but what if I use this
S = S1 x S2 using two analytical solutions of SDE? Why the drift term comes out incorrectly? Why can't I multiply two SDE solutions to get an equation for the third....?