Short Term Interest Rate Model Using Box-Cox Transformation

This paper propose a new short-term interest rate model having a different nonlinear drift function and the same diffusion coefficient with Chan et al. (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 $A\"{\i}t$-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.