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A positive interest rate model with sticky barrier

  • Yuri Kabanov
  • Masaaki Kijima
  • Sofiane Rinaz

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.

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

Volume (Year): 7 (2007)
Issue (Month): 3 ()
Pages: 269-284

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Handle: RePEc:taf:quantf:v:7:y:2007:i:3:p:269-284
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