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Mean Reversion Level Extensions of Time-Homogeneous Affine Term Structure Models

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  • Oh Kang Kwon

Abstract

It is well-known that time-homogeneous affine term structure models are incompatible with most observed initial forward rate curves. For the Vasicek (1977) and Cox et al. (1985) models, time-inhomogeneous extensions capable of fitting any given initial forward rate curve were introduced in Hull and White (1990), and similar extensions, for short rate models in general, were introduced in Bjork and Hyll (2000), Brigo and Mercurio (2001), and Kwon (2004). In this paper, we introduce a general and systematic method for obtaining time-inhomogeneous extensions of affine term structure models that are compatible with any observed initial forward rate curve. These extensions are minimal in the sense that the system of Riccati equations determining the bond prices remain essentially unchanged under the extension. Moreover, the extensions considered in Bjork and Hyll (2000), Brigo and Mercurio (2001), and Kwon (2004), for time-homogeneous affine term structure models, are all special cases of the extensions introduced in this paper.

Suggested Citation

  • Oh Kang Kwon, 2007. "Mean Reversion Level Extensions of Time-Homogeneous Affine Term Structure Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 291-302.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:291-302
    DOI: 10.1080/13504860600951686
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    References listed on IDEAS

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    1. 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..
    2. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. Damiano Brigo & Fabio Mercurio, 2001. "A deterministic-shift extension of analytically-tractable and time-homogeneous short-rate models," Finance and Stochastics, Springer, vol. 5(3), pages 369-387.
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    Cited by:

    1. Morelli, Giacomo & Santucci de Magistris, Paolo, 2019. "Volatility tail risk under fractionality," Journal of Banking & Finance, Elsevier, vol. 108(C).
    2. Oh Kwon, 2009. "On the equivalence of a class of affine term structure models," Annals of Finance, Springer, vol. 5(2), pages 263-279, March.

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