Reclaiming Quasi-Monte Carlo Efficiency in Portfolio Value-at-Risk Simulation Through Fourier Transform

Quasi-Monte Carlo methods overcome the problem of sample clustering in regular Monte Carlo simulation and have been shown to improve simulation efficiency in the derivatives pricing literature when the price is expressed as a multidimensional integration and the integrand is suitably smooth. For portfolio value-at-risk (VaR) problems, the distribution of portfolio value change is based on the expectation of an indicator function, hence the integrand is discontinuous. The purpose of this paper is to smooth the expectation estimation of an indicator function via Fourier transform so that the faster convergence rate of quasi-Monte Carlo methods can be reclaimed theoretically. Under fairly mild assumptions, the simulation of portfolio value-at-risk is fast and accurate. Numerical examples elucidate the advantage of the proposed approach over regular Monte Carlo and quasi-Monte Carlo methods.