Improved techniques for using Monte Carlo in VaR estimation

This paper is about the class of problems where a large number of VaR estimates, using Monte Carlo simulation, are required for different portfolios, drawn from a fixed universe of products with a fixed data generating process. We focus on the matrix–vector product which dominates the computational cost of this problem. We develop a series of results based on deriving bounds for different matrix norms, which allow us to eliminate rows from the matrix–vector product. Using these results, we propose fourteen alternative new algorithms. We compare them in a numerical experiment, and find that the best of these algorithms offers between 80% to 90% gains in speed. These algorithms make it quite feasible to do intra–day, real–time VaR calculations, using full Monte Carlo, on the derivatives exchanges with the highest trading intensities presently known, while requiring modest computer hardware.