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

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Listed:
  • 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, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0310009
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    References listed on IDEAS

    as
    1. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    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. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
    4. 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.
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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, EconWPA.
    2. 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.
    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, EconWPA, revised 25 Jan 2005.
    5. Marc Henrard, 2004. "Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model," Finance 0402008, EconWPA.
    6. Henrard, Marc, 2006. "Bonds futures: Delta? No gamma!," MPRA Paper 2249, University Library of Munich, Germany, revised 01 May 2006.
    7. 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.
    8. Marc Henrard, 2005. "Inflation bond option pricing in Jarrow-Yildirim model," Finance 0510027, EconWPA.
    9. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
    10. 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

    Keywords

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

    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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