Using Quasi-Monte Carlo Scenarios in Risk Management

We report on the use of quasi-random numbers in searching for worst-case scenarios of security portfolios. A systematic search for the worst-case scenario requires to find the global minimum of the portfolio-value function within a search domain of all plausible scenarios, which usually is an ellipsoid in the high dimensional space of risk factors. Equivalently, this optimization problem amounts to calculate the Maximum Loss of the portfolio at some plausibility threshold, which is a coherent risk measure often preferred to Value at Risk.

We compare the performance of three algorithms in order to assess the usefulness of low-discrepancy sequences for this optimization problem:
(1) a Monte Carlo search algorithm in the ellipsoid, (2) a Quasi-Monte Carlo search algorithm in the ellipsoid using Niederreiter-Xing sequences, and (3) the Multilevel Coordinate Search of W. Huyer and A. Neumaier applied to the transformed problem on the cube.