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Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas


  • Marc Henrard

    (Bank for International Settlements)


In practice the option pricing models are calibrated to market prices of liquid instruments. Consequently for those instruments, all the models give the same price. But the computed risk can be widely different. The note proposes comparison on simple instruments (swaptions) on a simple risk measure (first and second order sensitivity to the underlying yield curve). The main paper conclusion is that the hedging widely (up to 10\% of the underlying risk) between the model, specially with their dynamic. The shape of the smile has also an impact but to a lesser extend.

Suggested Citation

  • Marc Henrard, 2004. "Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas," Finance 0407018, University Library of Munich, Germany, revised 27 Sep 2005.
  • Handle: RePEc:wpa:wuwpfi:0407018
    Note: Type of Document - pdf; pages: 13. 13 pages, pdf Draft document, comments welcome

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    Cited by:

    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. Linus Kaisajuntti & Joanne Kennedy, 2014. "Stochastic volatility for interest rate derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 457-480, March.
    3. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in Levy term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 951-959.
    4. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in L\'evy term structure models," Papers 0902.3456,
    5. 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.

    More about this item


    Swaption; delta; hedging; in-the-model; out-of-the-model sensitivity; models difference;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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