Measuring Portfolio Risk Using Quasi Monte Carlo Methods

Abstract

We consider the application of Quasi Monte Carlo methods to risk measurement. A scenario generation technique based on low discrepancy Sobol sequences is compared to one based on pseudo-random number generation. The comparison methodology includes the calculation of the number of scenarios necessary to guarantee the required accuracy level of the Value-at-Risk estimate and the calculation of the relative performance of the two methods. The methodology is illustrated by a case study of a multi-currency portfolio. We demonstrate that Quasi Monte Carlo methods significantly improve the performance of the portfolio simulation and, therefore, reduce the time to obtain reliable risk measurements.