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Markov-functional interest rate models

Author

Listed:
  • Joanne Kennedy

    () (Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom)

  • Phil Hunt

    () (Global Derivatives and Fixed Income Markets, Westdeutsche Landesbank Girozentrale, 33/36 Gracechurch Street, London EC3V 0AX, United Kingdom)

  • Antoon Pelsser

    () (Structured Products Group , ABN-Amro Bank, P.O. Box 283, 1000 EA Amsterdam, The Netherlands and Department of Finance, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands Manuscript)

Abstract

We introduce a general class of interest rate models in which the value of pure discount bonds can be expressed as a functional of some (low-dimensional) Markov process. At the abstract level this class includes all current models of practical importance. By specifying these models in Markov-functional form, we obtain a specification which is efficient to implement. An additional advantage of Markov-functional models is the fact that the specification of the model can be such that the forward rate distribution implied by market option prices can be fitted exactly, which makes these models particularly suited for derivatives pricing. We give examples of Markov-functional models that are fitted to market prices of caps/floors and swaptions.

Suggested Citation

  • Joanne Kennedy & Phil Hunt & Antoon Pelsser, 2000. "Markov-functional interest rate models," Finance and Stochastics, Springer, vol. 4(4), pages 391-408.
  • Handle: RePEc:spr:finsto:v:4:y:2000:i:4:p:391-408
    Note: received: June 1999; final version received: August 1999
    as

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    References listed on IDEAS

    as
    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
    5. 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.
    6. J.E. Kennedy & P.J. Hunt, 1998. "Implied interest rate pricing models," Finance and Stochastics, Springer, vol. 2(3), pages 275-293.
    7. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.
    2. N. Moreni & A. Pallavicini, 2014. "Parsimonious HJM modelling for multiple yield curve dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 199-210, February.
    3. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    4. repec:spr:joptap:v:120:y:2004:i:3:d:10.1023_b:jota.0000025713.44548.71 is not listed on IDEAS
    5. Jirô Akahori & Andrea Macrina, 2012. "Heat Kernel Interest Rate Models With Time-Inhomogeneous Markov Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-15.
    6. Xiao Lin, 2016. "The Zero-Coupon Rate Model for Derivatives Pricing," Papers 1606.01343, arXiv.org.
    7. Junwu Gan, 2014. "An almost Markovian LIBOR market model calibrated to caps and swaptions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1937-1959, November.
    8. 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.
    9. Dan Pirjol, 2010. "Phase transition in a log-normal Markov functional model," Papers 1007.0691, arXiv.org, revised Jan 2011.
    10. Yuta Inoue & Takahiro Tsuchiya, 2011. "Defaultable Bonds via HKA," Papers 1103.4541, arXiv.org.
    11. repec:wsi:ijtafx:v:20:y:2017:i:02:n:s0219024917500091 is not listed on IDEAS
    12. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, University Library of Munich, Germany.
    13. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, Open Access Journal, vol. 3(4), pages 1-28, November.
    14. Albanese, Claudio, 2007. "Callable Swaps, Snowballs And Videogames," MPRA Paper 5229, University Library of Munich, Germany, revised 01 Oct 2007.
    15. Jiro Akahori & Yuji Hishida & Josef Teichmann & Takahiro Tsuchiya, 2009. "A Heat Kernel Approach to Interest Rate Models," Papers 0910.5033, arXiv.org.
    16. repec:wsi:ijtafx:v:20:y:2017:i:02:n:s0219024917500212 is not listed on IDEAS
    17. Mamon, Rogemar S., 2002. "A time-varying Markov chain model of term structure," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 309-312, December.
    18. C. D. D. Neumann, 2007. "On the structure of Gaussian pricing models and Gaussian Markov functional models," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 487-496.
    19. Simon H. Babbs, 2002. "Conditional Gaussian models of the term structure of interest rates," Finance and Stochastics, Springer, vol. 6(3), pages 333-353.
    20. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.

    More about this item

    Keywords

    Yield curve modelling; derivatives pricing; Markov processes;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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