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Generic Market Models

Author

Listed:
  • Raoul Pietersz

    (Erasmus University Rotterdam)

  • Marcel van Regenmortel

    (ABN AMRO Bank)

Abstract

Currently, there are two market models for valuation and risk management of interest rate derivatives, the LIBOR and swap market models. In this paper, we introduce arbitrage-free constant maturity swap (CMS) market models and generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. We develop generic expressions for the drift terms occurring in the stochastic differential equation driving the forward rates under a single pricing measure. The generic market model is particularly apt for pricing of Bermudan CMS swaptions, fixed-maturity Bermudan swaptions, and callable hybrid coupon swaps.

Suggested Citation

  • Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0502009
    Note: Type of Document - pdf; pages: 25
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    File URL: http://econwpa.repec.org/eps/fin/papers/0502/0502009.pdf
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    Other versions of this item:

    • 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.

    References listed on IDEAS

    as
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    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    4. Igor Grubisic & Raoul Pietersz, 2005. "Efficient Rank Reduction of Correlation Matrices," Finance 0502007, EconWPA.
    5. 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.
    6. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
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    8. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
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    10. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    11. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    12. Pietersz, R. & Pelsser, A.A.J., 2003. "Risk managing bermudan swaptions in the libor BGM model," Econometric Institute Research Papers EI 2003-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    14. Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 370-377.
    15. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, EconWPA.
    16. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    17. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
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    Citations

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    Cited by:

    1. Mark Davis & Vicente Mataix-Pastor, 2007. "Negative Libor rates in the swap market model," Finance and Stochastics, Springer, vol. 11(2), pages 181-193, April.
    2. 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.
    3. Ferdinando Ametrano & Mark Joshi, 2011. "Smooth simultaneous calibration of the LMM to caplets and co-terminal swaptions," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 547-558.
    4. Plat, Richard & Pelsser, Antoon, 2009. "Analytical approximations for prices of swap rate dependent embedded options in insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 124-134, February.
    5. 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.

    More about this item

    Keywords

    market model; generic market models; generic drift terms; hybrid products; BGM model;

    JEL classification:

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

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