Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-Monte Carlo methods in numerical finance
Management Science
Monto Carlo extension of quasi-Monte Carlo
Proceedings of the 30th conference on Winter simulation
Efficiency improvement by lattice rules for pricing Asian options
Proceedings of the 30th conference on Winter simulation
Variance Reduction via Lattice Rules
Management Science
Variance Reduction Techniques for Estimating Value-at-Risk
Management Science
Mathematical and Computer Modelling: An International Journal
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QuasiMonte 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 quasiMonte 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 quasiMonte Carlo methods.