Enterprise Risk Management Formula Book
6. Monte Carlo methods
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6.1 Creation of normal random variables
Box-Muller: if and are
independent standard uniform random variables, i.e. come from and then and are
independent standard normal random variables.
Polar method: if and are
independent random variables from , and then and are
independent standard normal random variables.
6.2 Cholesky
decomposition
If has real
entries, is symmetric and is positive definite then it can be decomposed as where is
a lower triangular matrix with strictly positive diagonal entries and is its
transpose. The entries of are:
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