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Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options

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  • Henrard, Marc

Abstract

A simple exotic option (floor on rolled deposit) is studied in the shifted log-normal Libor Market (LMM) and Gaussian HJM models. The shifted log-normal LMM exhibits a controllable volatility skew. An explicit approach is used for both models. Using approximations the price in the LMM is obtained without Monte Carlo simulation. The more precise approximation uses a twisted version of the perdictor-corrector adapted to explicit solutions. The results of the approximation are surprisingly good.

Suggested Citation

  • Henrard, Marc, 2007. "Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options," MPRA Paper 1534, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1534
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    File URL: https://mpra.ub.uni-muenchen.de/1534/1/MPRA_paper_1534.pdf
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    References listed on IDEAS

    as
    1. Marc Henrard, 2005. "Libor Market Model and Gaussian HJM explicit approaches to option on composition," Finance 0511016, University Library of Munich, Germany, revised 07 Dec 2005.
    2. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    3. Marc Henrard, 2006. "A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 1-18.
    4. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    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. Nielsen, Lars Tyge, 1999. "Pricing and Hedging of Derivative Securities," OUP Catalogue, Oxford University Press, number 9780198776192.
    7. 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.
    8. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    9. 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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    Cited by:

    1. Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
    2. Sander Willems, 2020. "SABR smiles for RFR caplets," Papers 2004.04501, arXiv.org, revised May 2020.

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    More about this item

    Keywords

    Libor Market Model; Heath-Jarrow-Morton; skew; smile; explicit solution; approximation; Bond Market Model; option on composition; existence results;
    All these keywords.

    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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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