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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xing Jin & Allen X. Zhang, 2006. "Reclaiming Quasi-Monte Carlo Efficiency in Portfolio Value-at-Risk Simulation Through Fourier Transform," Management Science, INFORMS, vol. 52(6), pages 925-938, June.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:6:p:925-938
    DOI: 10.1287/mnsc.1060.0505
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    References listed on IDEAS

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    Cited by:

    1. Halis Sak & .Ismail Bac{s}ou{g}lu, 2015. "Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk," Papers 1510.01593, arXiv.org.
    2. Borgonovo, Emanuele & Gatti, Stefano, 2013. "Risk analysis with contractual default. Does covenant breach matter?," European Journal of Operational Research, Elsevier, vol. 230(2), pages 431-443.
    3. Sak, Halis & Başoğlu, İsmail, 2017. "Efficient randomized quasi-Monte Carlo methods for portfolio market risk," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 87-94.
    4. Yu-Ying Tzeng & Paul M. Beaumont & Giray Ökten, 2018. "Time Series Simulation with Randomized Quasi-Monte Carlo Methods: An Application to Value at Risk and Expected Shortfall," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 55-77, June.
    5. Xiaoqun Wang & Ken Seng Tan, 2013. "Pricing and Hedging with Discontinuous Functions: Quasi-Monte Carlo Methods and Dimension Reduction," Management Science, INFORMS, vol. 59(2), pages 376-389, July.

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