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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