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Generalizations of Ho–Lee’s binomial interest rate model I: from one- to multi-factor

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  • Jirô Akahori

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  • Hiroki Aoki

    ()

  • Yoshihiko Nagata

    ()

Abstract

In this paper a multi-factor generalization of Ho–Lee model is proposed. In sharp contrast to the classical Ho–Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is a process with stationary independent increments to be compatible with principal component analysis. Based on the model, generalizations of duration-based hedging are proposed. A continuous-time limit of the model is also discussed. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Jirô Akahori & Hiroki Aoki & Yoshihiko Nagata, 2006. "Generalizations of Ho–Lee’s binomial interest rate model I: from one- to multi-factor," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(2), pages 151-179, June.
  • Handle: RePEc:kap:apfinm:v:13:y:2006:i:2:p:151-179 DOI: 10.1007/s10690-007-9039-8
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    References listed on IDEAS

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    1. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    2. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    4. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September.
    5. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    6. 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..
    7. Li Chen & Damir Filipović & H. Vincent Poor, 2004. "Quadratic Term Structure Models For Risk-Free And Defaultable Rates," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 515-536.
    8. 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.
    9. Jirô Akahori, 2005. "A discrete Itô calculus approach to He’s framework for multi-factor discrete markets," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, pages 273-287.
    10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
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    Cited by:

    1. Young Shin Kim & Stoyan Stoyanov & Svetlozar Rachev & Frank J. Fabozzi, 2017. "Another Look at the Ho-Lee Bond Option Pricing Model," Papers 1712.06664, arXiv.org.
    2. Laurini, Márcio Poletti & Ohashi, Alberto, 2015. "A noisy principal component analysis for forward rate curves," European Journal of Operational Research, Elsevier, vol. 246(1), pages 140-153.

    More about this item

    Keywords

    Ho–Lee model; Duration; Multi-factor; Recombining tree; Stationary increments; Forward rate; Drift condition; 91B28; 60G50; G12;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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