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Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models

  • Antonis Papapantoleon

    ()

    (TU Berlin, Institute of Mathematics)

  • John Schoenmakers

    ()

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • David Skovmand

    ()

    (Aarhus University, Department of Economics and Business and CREATES)

Registered author(s):

    The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIBOR model and aim at developing accurate and efficient log-Lévy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps and swaptions show that the approximations perform very well. In addition, we also consider the log-Lévy approximation of annuities, which offers good approximations for high volatility regimes.

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    File URL: ftp://ftp.econ.au.dk/creates/rp/11/rp11_22.pdf
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    Paper provided by Department of Economics and Business Economics, Aarhus University in its series CREATES Research Papers with number 2011-22.

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    Length: 33
    Date of creation: 04 Jun 2011
    Date of revision:
    Handle: RePEc:aah:create:2011-22
    Contact details of provider: Web page: http://www.econ.au.dk/afn/

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    1. 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.
    2. Antonis Papapantoleon & David Skovmand, 2010. "Picard Approximation of Stochastic Differential Equations and Application to Libor Models," CREATES Research Papers 2010-40, Department of Economics and Business Economics, Aarhus University.
    3. Denis Belomestny & John Schoenmakers, 2006. "A jump-diffusion Libor model and its robust calibration," SFB 649 Discussion Papers SFB649DP2006-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. 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.
    5. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    6. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    7. Tim Dunn & Erik Schlögl & Geoff Barton, 2000. "Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model," Research Paper Series 40, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, 07.
    9. 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 409-30, March.
    10. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    11. 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.
    12. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 327-344, December.
    13. Mark Joshi & Alan Stacey, 2008. "New and robust drift approximations for the LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 427-434.
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