medium · Quantitative Finance

Why is the Cholesky decomposition preferred over other matrix decompositions for generating correlated random variables in a quantitative simulation?

1. It is computationally efficient (taking roughly half the operations of LU) and naturally preserves the symmetry of the covariance matrix.
2. Cholesky is the only decomposition that is able to generate correlated random draws once more than two assets enter a simulation.
3. It allows the simulation to proceed even when the supplied covariance matrix is not positive definite, bypassing the eigenvalue check step.
4. It produces a diagonal output matrix, which greatly simplifies coding the coupled stochastic differential equations driving each correlated asset's path.

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