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Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model

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  • Marc Henrard

    (Bank for International Settlements)

Abstract

We present an explicit formula for European options on coupon bearing bonds and swaptions in the Heath-Jarrow-Morton (HJM) one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds. We provide also an explicit way to compute the hedging ratio (Delta) to hedge the option with its underlying.

Suggested Citation

  • Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0310009
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0310/0310009.pdf
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    References listed on IDEAS

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    1. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    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. 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. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Robert A. Jarrow & Arkadev Chatterjea, 2019. "The Heath–Jarrow–Morton Libor Model," World Scientific Book Chapters, in: An Introduction to Derivative Securities, Financial Markets, and Risk Management, chapter 25, pages 618-654, World Scientific Publishing Co. Pte. Ltd..
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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. Marc Henrard, 2004. "Semi-explicit Delta and Gamma for European swaptions in Hull- White one factor model," Finance 0411036, University Library of Munich, Germany, revised 25 Jan 2005.
    5. Ingo Beyna, 2013. "Interest Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, edition 127, number 978-3-642-34925-6, July.
    6. 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.
    7. 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.
    8. 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.
    9. Marc Henrard, 2004. "Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model," Finance 0402008, University Library of Munich, Germany.
    10. Henrard, Marc, 2006. "Bonds futures: Delta? No gamma!," MPRA Paper 2249, University Library of Munich, Germany, revised 01 May 2006.
    11. 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.
    12. Marc Henrard, 2005. "Inflation bond option pricing in Jarrow-Yildirim model," Finance 0510027, University Library of Munich, Germany.
    13. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.

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    More about this item

    Keywords

    Bond option; swaption; explicit formula; HJM model; one factor model; hedging;
    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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