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Generic market models

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  • Raoul Pietersz
  • Marcel Regenmortel

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.
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Suggested Citation

  • Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
    • Handle: RePEc:spr:finsto:v:10:y:2006:i:4:p:507-528
    DOI: 10.1007/s00780-006-0023-3
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    Other versions of this item:

    • 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.

    References listed on IDEAS

    as
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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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    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.
    13. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
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    15. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, University Library of Munich, Germany.
    16. 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, April.
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    19. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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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. 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.
    3. 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.
    4. 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.
    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, January.

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    More about this item

    Keywords

    Generic market model; Drift terms; BGM model; CMS; 91B28; 60H30; 60G44; G13;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics

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