Correlated-return simulation needs a factor that turns independent draws into the intended covariance structure. For a positive definite matrix, Cholesky supplies the triangular factor . The same factor also solves risk systems efficiently. This note shows the construction on a small matrix, the two triangular solves, and the limits of using numerical failure as a PD test.
Learning objectives. By the end of this note you should be able to:
- state the Cholesky factorisation and its shape/structure;
- use Cholesky to solve an SPD linear system via two triangular solves;
- use Cholesky as a positive-definiteness test;
- explain why Cholesky is the preferred numerical route over eigenvalue computation.
In this lesson
- The factorisation
- Solving via Cholesky, and using it as a test
Before you start
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