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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.

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File URL: http://128.118.178.162/eps/fin/papers/0310/0310009.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0310009.

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Date of creation: 12 Oct 2003
Date of revision:
Handle: RePEc:wpa:wuwpfi:0310009

Note: Type of Document - LaTeX; prepared on Linux; to print on HP;
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Web page: http://128.118.178.162

Related research

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

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References

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  1. 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 637-54, May-June.
  2. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  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. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
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Citations

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Cited by:
  1. Henrard, Marc, 2006. "Bonds futures: Delta? No gamma!," MPRA Paper 2249, University Library of Munich, Germany, revised 01 May 2006.
  2. Henrard, Marc, 2006. "TIPS Options in the Jarrow-Yildirim model," MPRA Paper 1423, University Library of Munich, Germany.
  3. Marc Henrard, 2005. "Inflation bond option pricing in Jarrow-Yildirim model," Finance 0510027, EconWPA.
  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. Henrard, Marc, 2007. "CMS swaps in separable one-factor Gaussian LLM and HJM model," MPRA Paper 3228, University Library of Munich, Germany.
  6. Marc Henrard, 2004. "Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model," Finance 0402008, EconWPA.
  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. "Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches," Finance 0505023, EconWPA.
  9. 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.

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