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

Xing Jin () and Allen X. Zhang ()
Additional contact information
Xing Jin: Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom
Allen X. Zhang: Freddie Mac, 1551 Park Run Drive, McLean, Virginia 22102

Management Science, 2006, vol. 52, issue 6, 925-938

Abstract: 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.

Keywords: quasi-Monte Carlo; portfolio; Fourier transform; value-at-risk (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (5)

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