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Interest rate option pricing with volatility humps

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  • Peter Ritchken
  • Iyuan Chuang

Abstract

This paper develops a simple model for pricing interest rate options when the volatility structure of forward rates is humped. Analytical solutions are developed for European claims and efficient algorithms exist for pricing American options. The interest rate claims are priced in the Heath-Jarrow-Morton paradigm, and hence incorporate full information on the term structure. The structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stationary. It is not possible to have all the above properties hold in a Heath Jarrow Morton model with a single state variable. It is shown that the full dynamics of the term structure is captured by a three state Markovian system. Caplet data is used to establish that the volatility hump is an important feature to capture. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Peter Ritchken & Iyuan Chuang, 2000. "Interest rate option pricing with volatility humps," Review of Derivatives Research, Springer, vol. 3(3), pages 237-262, October.
    • Handle: RePEc:kap:revdev:v:3:y:2000:i:3:p:237-262
    DOI: 10.1023/A:1009690621051
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    References listed on IDEAS

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    1. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
    2. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August.
    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.
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    5. 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..
    6. Narasimhan Jegadeesh & George Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
    7. Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. "Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-737, June.
    8. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    9. Robert R. Bliss & Peter Richken, 1996. "Empirical tests of two state-variable Heath-Jarrow models," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 452-481.
    10. 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.
    11. Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April.
    12. Balduzzi, Pierluigi & Bertola, Giuseppe & Foresi, Silverio, 1997. "A model of target changes and the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 39(2), pages 223-249, July.
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    Cited by:

    1. Haitao Li & Xiaoxia Ye, 2013. "A Type of HJM Based Affine Model: Theory and Empirical Evidence," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    2. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    3. Massimo Costabile & Ivar Massabó & Emilio Russo, 2013. "A Path-Independent Humped Volatility Model for Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 191-210, July.
    4. Marat Kramin & Saikat Nandi & Alexander Shulman, 2008. "A multi-factor Markovian HJM model for pricing American interest rate derivatives," Review of Quantitative Finance and Accounting, Springer, vol. 31(4), pages 359-378, November.
    5. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Post-Print hal-02367200, HAL.

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    Keywords

    interest rate claims; volatility humps;

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