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A positive interest rate model with sticky barrier

Author

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  • Yuri Kabanov
  • Masaaki Kijima
  • Sofiane Rinaz

Abstract

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait for a random time until the rate is reinitialized to a (possibly random) strictly positive value. This setting ensures that all term rates are strictly positive. Our objective is to provide a simple method to price zero-coupon bonds. A basic statistical study of the data at hand indeed suggests a switch to a different mode of behaviour when we get to a low level of interest rates. We introduce a variable for the time already spent at 0 (during the last stay) and derive the pricing equation for the bond. We then solve this partial integro-differential equation (PIDE) on its entire domain using a finite difference method (Cranck-Nicholson scheme), a method of characteristics and a fixed point algorithm. Resulting yield curves can exhibit many different shapes, including the S shape observed on the recent Japanese market.

Suggested Citation

  • Yuri Kabanov & Masaaki Kijima & Sofiane Rinaz, 2007. "A positive interest rate model with sticky barrier," Quantitative Finance, Taylor & Francis Journals, vol. 7(3), pages 269-284.
    • Handle: RePEc:taf:quantf:v:7:y:2007:i:3:p:269-284
    DOI: 10.1080/14697680600999351
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Ravi Bansal & Hao Zhou, 2002. "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, American Finance Association, vol. 57(5), pages 1997-2043, October.
    3. Licheng Sun, 2003. "Nonlinear Drift And Stochastic Volatility: An Empirical Investigation Of Short‐Term Interest Rate Models," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 26(3), pages 389-404, September.
    4. Asbjørn T. Hansen & Rolf Poulsen, 2000. "A simple regime switching term structure model," Finance and Stochastics, Springer, vol. 4(4), pages 409-429.
    5. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    6. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    7. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    8. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    9. 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.
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    Cited by:

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    2. Wagner, Stefan, 2024. "Orthogonal intertwiners for infinite particle systems in the continuum," Stochastic Processes and their Applications, Elsevier, vol. 168(C).

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