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Yes, Libor Models can capture Interest Rate Derivatives Skew : A Simple Modelling Approach

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  • Eymen Errais

    ()
    (Managment Science and Engineering Stanford University)

  • Fabio Mercurio
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    Abstract

    We introduce a simple extension of a shifted geometric Brownian motion for modelling forward LIBOR rates under their canonical measures. The extension is based on a parameter uncertainty modelled through a random variable whose value is drawn at an in¯nitesimal time after zero. The shift in the proposed model captures the skew commonly seen in the cap market, whereas the uncertain volatility component allows us to obtain more symmetric implied volatility structures. We show how this model can be calibrated to cap prices. We also propose an analytical approximated formula to price swaptions from the cap calibrated model. Finally, we build the bridge between caps and swaptions market by calibrating the correlation structure to swaption prices, and analysing some implications of the calibrated model parameters

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    File URL: http://repec.org/sce2005/up.30400.1107018088.pdf
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    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 192.

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    Date of creation: 11 Nov 2005
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    Handle: RePEc:sce:scecf5:192

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    Related research

    Keywords: Libor Models; Volatility Skew; Interest Rate Derivatives;

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    1. 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.
    2. Feng Zhao & Robert Jarrow & Haitao Li, 2004. "Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?," Econometric Society 2004 North American Winter Meetings 431, Econometric Society.
    3. Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-84.
    4. 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.
    5. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    6. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-85.
    7. 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.
    8. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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    Cited by:
    1. Marc Henrard, 2005. "Libor Market Model and Gaussian HJM explicit approaches to option on composition," Finance 0511016, EconWPA, revised 07 Dec 2005.

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