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Arbitrary Initial Term Structure within the CIR Model: A Perturbative Solution

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  • Carlo Mari
  • Roberto Reno

Abstract

Single-factor interest rate models with constant coefficients are not consistent with arbitrary initial term structures. An extension which allows both arbitrary initial term structure and analytical tractability has been provided only in the Gaussian case. In this paper, within the context of the HJM methodology, an extension of the CIR model is provided which admits arbitrary initial term structure. It is shown how to calculate bond prices via a perturbative approach, and closed formulas are provided at every order. Since the parameter selected for the expansion is typically estimated to be small, the perturbative approach turns out to be adequate to our purpose. Using results on affine models, the extended CIR model is estimated via maximum likelihood on a time series of daily interest rate yields. Results show that the CIR model has to be rejected with respect to the proposed extension, and it is pointed out that the extended CIR model provides a more flexible characterization of the link between risk neutral and natural probability.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 13 (2006)
Issue (Month): 2 ()
Pages: 143-153

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Handle: RePEc:taf:apmtfi:v:13:y:2006:i:2:p:143-153

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  1. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
  2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  3. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
  4. 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.
  5. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(04), pages 619-642, December.
  6. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
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Cited by:
  1. Antonio Mannolini & Carlo Mari & Roberto Ren�, 2008. "Pricing caps and floors with the extended CIR model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(4), pages 386-400.

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