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The Markov-switching jump diffusion LIBOR market model

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  • L. Steinruecke
  • R. Zagst
  • A. Swishchuk

Abstract

In this paper, we introduce an extension to the LIBOR Market Model (LMM) that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LMM by a regime-switching jump diffusion. We demonstrate that the new Markov-switching jump diffusion (MSJD) LMM can be embedded into a generalized regime-switching Heath-Jarrow-Morton model and prove that the considered market is arbitrage-free. We derive pricing formulas for caps, floors and swaptions using Fourier pricing techniques and show how the model can be calibrated to real market data.

Suggested Citation

  • L. Steinruecke & R. Zagst & A. Swishchuk, 2015. "The Markov-switching jump diffusion LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 455-476, March.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:3:p:455-476
    DOI: 10.1080/14697688.2014.962594
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    References listed on IDEAS

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    1. Denis Belomestny & John Schoenmakers, 2010. "A jump-diffusion Libor model and its robust calibration," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 529-546.
    2. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    4. Mark Joshi & Riccardo Rebonato, 2003. "A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementation," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 458-469.
    5. 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..
    6. 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.
    7. Riccardo Rebonato, 2003. "Which Process Gives Rise To The Observed Dependence Of Swaption Implied Volatility On The Underlying?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 419-442.
    8. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    9. 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.
    10. Riccardo Rebonato & Mark Joshi, 2002. "A Joint Empirical And Theoretical Investigation Of The Modes Of Deformation Of Swaption Matrices: Implications For Model Choice," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(07), pages 667-694.
    11. Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997. "Towards a general theory of bond markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 141-174.
    12. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    13. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    14. Philip Gray, 2002. "Bayesian estimation of financial models," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 42(2), pages 111-130, June.
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    Cited by:

    1. Robert J. Elliott & Tak Kuen Siu, 2016. "Pricing regime-switching risk in an HJM interest rate environment," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1791-1800, December.

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