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Toward real-time pricing of complex financial derivatives

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  • S. Ninomiya
  • S. Tezuka
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    Abstract

    In this paper, we investigate the feasibility of using low-discrepancy sequences to allow complex derivatives, such as mortgage-backed securities (MBSs) and exotic options, to be calculated considerably faster than is possible by using conventional Monte Carlo methods. In our experiments, we examine classical classes of low-discrepancy sequences, such as Halton, Sobol', and Faure sequences, as well as the very recent class called generalized Niederreiter sequences, in the light of the actual convergence rate of numerical integration with practical numbers of dimensions. Our results show that for the problems of pricing financial derivatives that we tested: (1) generalized Niederreiter sequences perform markedly better than both classical sequences and Monte Carlo methods; and (2) classical low-discrepancy sequences often perform worse than Monte Carlo methods. Finally, we discuss several important research issues from both practical and theoretical viewpoints.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 3 (1996)
    Issue (Month): 1 ()
    Pages: 1-20

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    Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:1-20

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    Related research

    Keywords: low-discrepancy sequences; generalized Niederreiter sequences; Faure sequences; Sobol' sequences; financial derivatives;

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    Cited by:
    1. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer, vol. 20(2), pages 147-182, May.
    2. 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.
    3. Tsutomu Tamura, 2005. "Comparison of randomization techniques for low-discrepancy sequences in finance," Asia-Pacific Financial Markets, Springer, vol. 12(3), pages 227-244, September.
    4. Josh Lerner, 2004. "Where Does State Street Lead? First Look at Finance Patents, 1971-2000," Levine's Working Paper Archive 122247000000000497, David K. Levine.
    5. 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.
    6. 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.
    7. 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.
    8. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.

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