Does the Short Rate Revert to its Mean in the Risk-Neutral World?

Abstract

We propose a methodology to calibrate the non-linear and non-affine short rate models under physical and risk-neutral probability measures, based on the U.S treasury yield curve data. For this purpose, we price the default-free bond using the Markov chain approximation method built on the well-established idea of local consistency. Integrating the standard recursive filtering algorithm and the Markov chain approximation bond price formula, we propose a Markov chain filter in which the transition equation is a general stochastic differential equation for the short rate dynamics, and the measurement equation can be based on observations of any interest rate derivatives. Our simulation experiments show that popular parameter estimators can generate spurious non-linear drift estimates. However, the proposed Markov chain filter does not. In contrast to the existing literature, through our empirical findings we argue that the short rate does not revert to its mean under the risk-neutral probability measure. Our findings corroborate the observations that yields on the short end term structure have remained near 0% for more than 30 months since the implementation of Quantitative Easing monetary policy.