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Generic Market Models

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/fin/papers/0502/0502009.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0502009.

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Length: 25 pages
Date of creation: 11 Feb 2005
Date of revision:
Handle: RePEc:wpa:wuwpfi:0502009

Note: Type of Document - pdf; pages: 25
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Web page: http://128.118.178.162

Related research

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

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References

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  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
  2. S.Galluccio & Z. Huang & J.-M. Ly & O. Scaillet, 2005. "Theory and Calibration of Swap Market Models," FAME Research Paper Series rp107, International Center for Financial Asset Management and Engineering.
  3. Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
  4. Stefano Galluccio & Christopher Hunter, 2004. "The Co-initial Swap Market Model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 33(2), pages 209-232, 07.
  5. Rubinstein, Mark, 1983. " Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-17, March.
  6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  7. Raoul Pietersz & Antoon Pelsser, 2005. "Risk Managing Bermudan Swaptions in the Libor BGM Model," Finance 0502004, EconWPA.
  8. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
  9. 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.
  10. Igor Grubisic & Raoul Pietersz, 2005. "Efficient Rank Reduction of Correlation Matrices," Finance 0502007, EconWPA.
  11. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
  12. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
  13. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, EconWPA.
  14. Erik Schlögl, 1999. "A Multicurrency Extension of the Lognormal Interest Rate Market Models," Research Paper Series 20, Quantitative Finance Research Centre, University of Technology, Sydney.
  15. 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.
  16. Pietersz, R. & Groenen, P.J.F., 2004. "Rank reduction of correlation matrices by majorization," Econometric Institute Research Papers EI 2004-11, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  17. 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.
  18. 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. 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. 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.
  3. 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.

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