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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. 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.
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    Cited by:

    1. Hidenori Futami, 2009. "Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(4), pages 347-369, December.

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