Monte Carlo for Value at Risk

Monte Carlo simulations are widely used in pricing and risk management of complex financial instruments. Recently, quasi-Monte Carlo methods, which are deterministic methods because they are based on low discrepancy sequences, have been found far superior to Monte Carlo for pricing of financial derivatives in terms of both speed and accuracy. In this paper we address the application of these deterministic methods to risk management. Our study compares the efficacy of deterministic simulation, using low discrepancy sequences, with Monte Carlo for the computation of Value at Risk (VaR). In particular, we show how the deterministic methods can be applied to the computation of VaR and that they converge faster than Monte Carlo. We illustrate our findings with two tests. The first of our tests uses a portfolio of equity and currency european call options. The second test uses a portfolio of collateralized mortgage obligation tranches. The low discrepancy sequence chosen for our tests is the generalized Faure sequence due to Tezuka [1995]. VaR in brief Market risk has become one of the most popular buzzwords of the financial markets. Regulators, commercial and investment banks, corporate and institutional investors are increasingly focusing on measuring more precisely the level of market risk incurred by their institutions. Market risk is the uncertainty of future returns due to fluctuations of financial asset quantities such as stock prices, interest rates, exchange rates, and commodity prices. One of the most widely accepted concepts in market risk management is Value at Risk. Risk management systems based on VaR have been designed and implemented in many financial institutions, asset management institutions, and non-financial