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Libor Market Model and Gaussian HJM explicit approaches to option on composition

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  • Marc Henrard

    (Bank for International Settlements)

Abstract

The twin brothers Libor Market and Gaussian HJM models are investigated. A simple exotic option, floor on composition, is studied. The same explicit approach is used for both models. Using an approximation the LLM price is obtained without Monte Carlo simulation. The results of the approximation are very good, with an error well below the uncertainty due to the simulation. The appendices proves the existence of the (modified) normal and shifted log-normal LLM used in the pricing. The link of the latter with the Ho and Lee continuous time model is described.

Suggested Citation

  • 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.
    • Handle: RePEc:wpa:wuwpfi:0511016
    Note: Type of Document - pdf; pages: 11. Draft version, comments welcome
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0511/0511016.pdf
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    References listed on IDEAS

    as
    1. 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..
    2. Eymen Errais & Fabio Mercurio, 2005. "Yes, Libor Models can capture Interest Rate Derivatives Skew : A Simple Modelling Approach," Computing in Economics and Finance 2005 192, Society for Computational Economics.
    3. 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.
    4. Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, University Library of Munich, Germany, revised 27 Sep 2005.
    5. 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).
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    1. Henrard, Marc, 2007. "Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options," MPRA Paper 1534, University Library of Munich, Germany.

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    More about this item

    Keywords

    explicit formula; Libor market model; HJM model; shifted log-normal model; normal model; existence; option on composition;
    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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