This paper propose a new short-term interest rate model having a different
nonlinear drift function and the same diffusion coefficient with Chan, Karolyi,
Longstaff, and Sanders (1992) model. The fractional polynomial power of the drift
function in our model is linked to the local volatility elasticity of the diffusion coefficient.
While the nonlinear drift function estimated by A¨ıt-Sahalia (1996a) and others
has a feature that higher interest rates tend to revert downward and low rates upward,
the drift function estimated by our nonlinear model shows that higher interest rate
mean-reverts strongly, but, medium rates has almost zero drift and low rates has a
very small drift. This characteristic coincides the empirical result based on the nonparametric
methodology by Stanton (1997) and the implication by the scatter plot of
the short rate data. Furthermore, if our model is transformed to make the diffusion
process have a constant term, the drift term in our model is very similar to that in
A¨ıt-Sahalia model. In the viewpoint of data, while his model is applied to the original
interest rate data, our model is applied to the transformed data.
Keywords: Short-term interest rate model; Box-Cox transformation