New answers tagged correlation
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Define $W(t)=\frac{W_1(t)-\rho W_2(t)}{\sqrt{1-\rho^2}}$, and use Levy characterization of brownien motion.
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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 &...
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