Generating Correlated Realizations Without Matrix Decomposition

Abstract

Practical bank counterparty credit risk is determined by means of Monte Carlo simulations projecting the counterparty portfolio future mark to markets. In principle the simulations have to be applied to every counterparty across all bank and derivatives books so the projections depend on a large number of correlated interest rate, FX, commodity, credit and equity risk factors. The traditional simulation approach for generating correlated random numbers employs correlation matrix decomposition however for a large bank the size of the correlation matrix makes decomposition very problematic or impossible. This paper discusses a simple algorithm that creates appropriately correlated realizations solely from independent random numbers and historical data points thereby avoiding the need for matrix decomposition.

Keywords: counterparty credit risk, Monte Carlo simulation, CVA, EPE, EE, EC