# Tag Info

Define $W(t)=\frac{W_1(t)-\rho W_2(t)}{\sqrt{1-\rho^2}}$, and use Levy characterization of brownien motion.
The usual ansatz for these kind of setups is to find those components of a Cholesky decomposition of the correlation matrix of your stochastic drivers $dW_{S_1}, dW_{S_2}, dW_{V_1}, dW_{V_2}$ such that all conditions are fulfilled. Let us assume a 4x4 correlation matrix $R$ that we decompose using Cholesky to  L(R) = \begin{pmatrix} 1 & 0 & 0 &...