Correlated Monte Carlo Simulation using Cholesky Decomposition
20 Pages Posted: 4 May 2022 Last revised: 13 May 2022
Date Written: March 25, 2022
Abstract
In this paper we outline the steps necessary to perform Monte Carlo simulation with multiple correlated assets using Cholesky Decomposition. First we illustrate how to perform Monte Carlo simulation on a single asset. Secondly we look at Monte Carlo simulation for multiple assets that are correlated. Thirdly we discuss how to introduce asset correlation and finally we outline how to use Cholesky Decomposition to generate correlated random variables for Monte Carlo simulation including how to compute the correlation lower diagonal matrix.
Keywords: Multi-Dimensional, Monte Carlo, Simulation, Correlation, Brownian Motion, Ito's Lemma, Cholesky Decomposition, Correlated Random Variables
JEL Classification: C15, C22, C53, C73, F17, G12, G15
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