Which of the following techniques is used to generate multivariate normal random numbers that are correlated?

Which of the following techniques is used to generate multivariate normal random numbers that are correlated?
A . Simulation
B . Markov process
C . Cholesky decomposition of the correlation matrix
D . Pseudo random number generator

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Answer: C

Explanation:

A PRNG (pseudorandom number generators of the kind included in statistical packages and Excel) is used to generate random numbers that are not correlated with each other, ie they are random. A Markov process is a stochastic model that depends only upon its current state. Simulation underlies many financial calculations. None of these directly relate to generating correlated multivariate normal random numbers. That job is done utilizing a Cholesky decomposition of the correlation matrix.

Specifically, a Cholesky decomposition involves the factorization of the correlation matrix into a lower triangular matrix (a square matrix all of whose entries above the diagonal are zero) and its transpose. This can then be combined with random numbers to generate a set of correlated normal random numbers. This technique is used for calculating Monte Carlo VaR.