Using the Hidden Markov Model to Improve the Hull-White Model for Short Rate

Abstract

We report a modeling study of short term interest rates using the Hidden Markov Model (HMM) and the Hull-White (HW) model. For this purpose, we modify the original HW model by adding a regime variable to its instantaneous forward function. This variable is defined by the regimes of the short term interest rate which are found by a two-state HMM. The combination of the HMM and the HW model for generating interest rate predictions results in a significant improvement, reducing the error of the estimations by about 50% compared to that of using HW alone. Furthermore, the errors of the simulations using HMM and HW have a smaller standard deviation compare with which of using the HW. Adjusted R-square results also show that the regime variable is significant. This improvement to the short-term interest rate model has a substantial impact on financial economics and related fields.