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Consistency conditions for affine term structure models

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  • Sergei Levendorskii

Abstract

ATSM are widely applied for pricing of bonds and interest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open question. First, the standard approach to ATSM uses the Feynman-Kac theorem which is easily applicable only when r is bounded from below. Second, if the tuple of state variables belongs to the region where r is positive, the bond price should decrease in any state variable for which the corresponding coefficient in the formula for r is positive; the bond price should also decrease as the time to maturity increases. In the paper, sufficient conditions for the application of the Feynman-Kac formula, and monotonicity of the bond price are derived, for wide classes of affine term structure models in the pure diffusion case. Necessary conditions for the monotonicity are obtained as well. The results can be generalized for jump-diffusion processes.

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  • Sergei Levendorskii, 2004. "Consistency conditions for affine term structure models," Papers cond-mat/0404107, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0404107
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    Cited by:

    1. Christian Gourieroux & Razvan Sufana, 2006. "A Classification of Two-Factor Affine Diffusion Term Structure Models," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 31-52.
    2. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    3. Sergei LevendorskiĬ, 2006. "Consistency conditions for affine term structure models," Annals of Finance, Springer, vol. 2(2), pages 207-224, March.
    4. Kimmel, Robert L., 2007. "Complex Times: Asset Pricing and Conditional Moments under Non-affine Diffusions," Working Paper Series 2007-6, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    5. Sergei Levendorskiĭ, 2022. "Operators and Boundary Problems in Finance, Economics and Insurance: Peculiarities, Efficient Methods and Outstanding Problems," Mathematics, MDPI, vol. 10(7), pages 1-36, March.

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