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Toward real-time pricing of complex financial derivatives

Author

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  • S. Ninomiya
  • S. Tezuka

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.

Suggested Citation

  • S. Ninomiya & S. Tezuka, 1996. "Toward real-time pricing of complex financial derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 1-20.
  • Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:1-20
    DOI: 10.1080/13504869600000001
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    Citations

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    Cited by:

    1. Fredrik Ã…kesson & John P. Lehoczky, 2000. "Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities," Management Science, INFORMS, vol. 46(9), pages 1171-1187, September.
    2. Ninomiya, Syoiti, 2003. "A new simulation scheme of diffusion processes: application of the Kusuoka approximation to finance problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 479-486.
    3. Tsutomu Tamura, 2005. "Comparison of randomization techniques for low-discrepancy sequences in finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(3), pages 227-244, September.
    4. 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.
    5. Eichler Andreas & Leobacher Gunther & Zellinger Heidrun, 2011. "Calibration of financial models using quasi-Monte Carlo," Monte Carlo Methods and Applications, De Gruyter, vol. 17(2), pages 99-131, January.
    6. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(2), pages 147-182, May.
    7. Josh Lerner, 2000. "Where Does State Street Lead? A First Look at Finance Patents, 1971-2000," NBER Working Papers 7918, National Bureau of Economic Research, Inc.
    8. 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.
    9. Ninomiya Syoiti, 2003. "A partial sampling method applied to the Kusuoka approximation," Monte Carlo Methods and Applications, De Gruyter, vol. 9(1), pages 27-38, January.
    10. 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.
    11. 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.
    12. 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.
    13. 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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