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Fast drift approximated pricing in the BGM model

Author

Listed:
  • Raoul Pietersz

    (Erasmus University Rotterdam)

  • Antoon Pelsser

    (Erasmus University Rotterdam)

  • Marcel van Regenmortel

    (ABN AMRO Bank)

Abstract

This paper shows that the forward rates process discretized by a single time step together with a separability assumption on the volatility function allows for representation by a low-dimensional Markov process. This in turn leads to e±cient pricing by for example finite differences. We then develop a discretization based on the Brownian bridge especially designed to have high accuracy for single time stepping. The scheme is proven to converge weakly with order 1. We compare the single time step method for pricing on a grid with multi step Monte Carlo simulation for a Bermudan swaption, reporting a computational speed increase of a factor 10, yet pricing sufficiently accurate.

Suggested Citation

  • Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0502005
    Note: Type of Document - pdf; pages: 37
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0502/0502005.pdf
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    References listed on IDEAS

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    7. Björk, Tomas & Landén, Camilla & Svensson, Lars, 2002. "Finite dimensional Markovian realizations for stochastic volatility forward rate models," SSE/EFI Working Paper Series in Economics and Finance 498, Stockholm School of Economics, revised 07 May 2002.
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Raoul Pietersz & Antoon Pelsser, 2010. "A comparison of single factor Markov-functional and multi factor market models," Review of Derivatives Research, Springer, vol. 13(3), pages 245-272, October.
    2. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
      • Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, University Library of Munich, Germany.
      • Pietersz, R. & van Regenmortel, M., 2005. "Generic Market Models," ERIM Report Series Research in Management ERS-2005-010-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
    4. S. Galluccio & J.‐M. Ly & Z. Huang & O. Scaillet, 2007. "Theory And Calibration Of Swap Market Models," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 111-141, January.
    5. Christian Fries & Joerg Kampen, 2010. "Global existence, regularity and a probabilistic scheme for a class of ultraparabolic Cauchy problems," Papers 1002.5031, arXiv.org, revised Oct 2012.
    6. Jaka Gogala & Joanne E. Kennedy, 2017. "CLASSIFICATION OF TWO- AND THREE-FACTOR TIME-HOMOGENEOUS SEPARABLE LMMs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-44, March.
    7. Ronald Hochreiter & Georg Pflug, 2006. "Polynomial Algorithms for Pricing Path-Dependent Interest Rate Instruments," Computational Economics, Springer;Society for Computational Economics, vol. 28(3), pages 291-309, October.
    8. Mark Joshi & Alan Stacey, 2008. "New and robust drift approximations for the LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 427-434.

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    More about this item

    Keywords

    BGM model; predictor-corrector; Brownian bridge; Markov processes; separability; Feynman-Kac; Bermudan swaption;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

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