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Quasi-Monte Carlo Methods in Numerical Finance

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Author Info

  • Corwin Joy

    (Enron Corporation, 1400 Smith Street, Houston, Texas 77002-7361)

  • Phelim P. Boyle

    (School of Accountancy, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada)

  • Ken Seng Tan

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada)

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    Abstract

    This paper introduces and illustrates a new version of the Monte Carlo method that has attractive properties for the numerical valuation of derivatives. The traditional Monte Carlo method has proven to be a powerful and flexible tool for many types of derivatives calculations. Under the conventional approach pseudo-random numbers are used to evaluate the expression of interest. Unfortunately, the use of pseudo-random numbers yields an error bound that is probabilistic which can be a disadvantage. Another drawback of the standard approach is that many simulations may be required to obtain a high level of accuracy. There are several ways to improve the convergence of the standard method. This paper suggests a new approach which promises to be very useful for applications in finance. Quasi-Monte Carlo methods use sequences that are deterministic instead of random. These sequences improve convergence and give rise to deterministic error bounds. The method is explained and illustrated with several examples. These examples include complex derivatives such as basket options, Asian options, and energy swaps.

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    File URL: http://dx.doi.org/10.1287/mnsc.42.6.926
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 42 (1996)
    Issue (Month): 6 (June)
    Pages: 926-938

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    Handle: RePEc:inm:ormnsc:v:42:y:1996:i:6:p:926-938

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    Related research

    Keywords: Monte Carlo simulation; quasi-random sequences; Faure sequences; numerical finance; derivative valuation;

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    Cited by:
    1. Raimova, Gulnora, 2011. "Variance reduction methods at the pricing of weather options," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 21(1), pages 3-15.
    2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    3. Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October.
    4. Armstrong, Michael J., 2001. "The reset decision for segregated fund maturity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 257-269, October.
    5. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    6. David Heath & Eckhard Platen, 2002. "A Variance Reduction Technique Based on Integral Representations," Research Paper Series 75, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Han, Chuan-Hsiang & Lai, Yongzeng, 2010. "A smooth estimator for MC/QMC methods in finance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 536-550.
    8. Okten, Giray & Eastman, Warren, 2004. "Randomized quasi-Monte Carlo methods in pricing securities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2399-2426, December.
    9. Boyle, Phelim & Imai, Junichi & Tan, Ken Seng, 2008. "Computation of optimal portfolios using simulation-based dimension reduction," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 327-338, December.
    10. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    11. Siegl, Thomas & F. Tichy, Robert, 2000. "Ruin theory with risk proportional to the free reserve and securitization," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 59-73, February.
    12. Rose, Simon, 1998. "Valuation of Interacting Real Options in a Tollroad Infrastructure Project," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 711-723.
    13. Patrick Leoni, 2007. "Monte-Carlo Estimations of the Downside Risk of Derivative Portfolios," Economics, Finance and Accounting Department Working Paper Series n1760607, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.

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