Adaptive Interest Rate Modelling

A good description of the dynamic process of interest rates is crucial to price derivatives and to hedge corresponding risk. An unstable macroeconomic context motivates the stochastic interest rate models with time‐varying parameters. In this paper, the local parameter approach is introduced to adaptively estimate interest rate models. This method can be generally used in time‐varying coefficient parametric models. It is used not only to detect jumps and structural breaks but also to choose the largest time homogeneous interval for each time point, such that in this interval the coefficients are statistically constant. We apply this adaptive approach in both simulations and real data analysis. Using the 3‐month Treasury bill rate as a proxy of the short rate, we find that our method can detect the structural breaks as well as the stable intervals for homogeneously modelling of the interest rate process. The time homogeneous interval cannot persist in an unstable macroeconomy. Furthermore, our approach performs well in long horizon forecasting.