On The Calibration of Short-Term Interest Rates Through a CIR Model

Abstract: It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates. Moreover, the diffusion term in the rate dynamics goes to zero when short rates are small; both volatility and long-run mean do not change with time; they do not fit with the skewed (fat tails) distribution of the interest rates, etc. The aim of the present work is to suggest a new framework, which we call the CIR# model, that well fits the term structure of short interest rates so that the market volatility structure is preserved as well as the analytical tractability of the original CIR model.