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Bonds futures: Delta? No gamma!

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  • Henrard, Marc

Abstract

Bond futures are liquid but complex instruments. Here they are analysed in a one-factor Gaussian HJM model. The in-the-model delta and out-of-the-model delta and gamma are studied. An explicit formula is provided for in-the-model delta. The out-of-the-model delta and gamma are equivalent to partial derivatives with respect to discount factors. In particular cases the derivative can not be obtained by standard techniques. The same situations lead to cases where the gammas (second order partial derivatives) do not exists.

Suggested Citation

  • Henrard, Marc, 2006. "Bonds futures: Delta? No gamma!," MPRA Paper 2249, University Library of Munich, Germany, revised 01 May 2006.
    • Handle: RePEc:pra:mprapa:2249
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    File URL: https://mpra.ub.uni-muenchen.de/2249/1/MPRA_paper_2249.pdf
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    References listed on IDEAS

    as
    1. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    2. 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..
    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. Henrard, Marc, 2006. "Bonds futures and their options: more than the cheapest-to-deliver; quality option and marginning," MPRA Paper 2001, University Library of Munich, Germany.
    5. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
    6. Marc Henrard, 2003. "Explicit Bond Option Formula In Heath–Jarrow–Morton One Factor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 57-72.
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    1. Henrard, Marc, 2006. "Bonds futures and their options: more than the cheapest-to-deliver; quality option and marginning," MPRA Paper 2001, University Library of Munich, Germany.

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    More about this item

    Keywords

    Bond future; delivery option; delta; gamma; HJM gaussian model; in-the-model; out-of-the-model;
    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

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