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Explicit Bond Option Formula In Heath–Jarrow–Morton One Factor Model

Author

Listed:
  • MARC HENRARD

    (Banking Department, Bank for International Settlements, Aeschenplatz 1, CH-4002 Basel, Switzerland)

Abstract

We hereby present an explicit formula for European options on coupon bearing bonds in the Heath–Jarrow–Morton one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds for special form of volatility. Moreover we present a formula for zero-coupon bonds without condition on the volatility. We provide also an explicit way to compute the hedging ratio (Δ) in order to hedge the options individually.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:01:n:s0219024903001785
    DOI: 10.1142/S0219024903001785
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    Citations

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    Cited by:

    1. Marc Henrard, 2005. "Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches," Finance 0505023, University Library of Munich, Germany.
    2. Bünyamin Erkan & Jean-Luc Prigent, 2020. "About Long-Term Cross-Currency Bermuda Swaption Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 239-262, June.
    3. Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
    4. Ingo Beyna, 2013. "Interest Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, edition 127, number 978-3-642-34925-6, October.
    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.
    6. Marcin Dec, 2019. "Markovian and multi-curve friendly parametrisation of a HJM model used in valuation adjustment of interest rate derivatives," Bank i Kredyt, Narodowy Bank Polski, vol. 50(2), pages 107-148.
    7. Ingo Beyna & Carl Chiarella & Boda Kang, 2012. "Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time," Research Paper Series 317, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Marc Henrard, 2004. "Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model," Finance 0402008, University Library of Munich, Germany.
    9. Henrard, Marc, 2006. "Bonds futures: Delta? No gamma!," MPRA Paper 2249, University Library of Munich, Germany, revised 01 May 2006.
    10. 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.
    11. Marc Henrard, 2005. "Inflation bond option pricing in Jarrow-Yildirim model," Finance 0510027, University Library of Munich, Germany.
    12. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.

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