medium · Quantitative Finance numerical
Why is the Cholesky decomposition preferred over other matrix decompositions for generating correlated random variables in a quantitative simulation?
- It is computationally efficient (taking roughly half the operations of LU) and naturally preserves the symmetry of the covariance matrix.
- Cholesky is the only decomposition that is able to generate correlated random draws once more than two assets enter a simulation.
- It allows the simulation to proceed even when the supplied covariance matrix is not positive definite, bypassing the eigenvalue check step.
- 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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