Estimation and empirical evaluation of the time-dependent Extended-CIR term structure model

Abstract

Empirical study of 25 years US Treasury bills data shows that even when the spot interest rate remains fixed, its volatility varies significantly over time. Constant-coefficient models cannot capture these changes as they give rise to time-homogeneous distributions. Maximum likelihood fitting of a one-factor time-dependent Extended-CIR model of the term structure, whose closed-form solution was previously obtained by the author, shows that it can capture these changes, as well as achieve significantly higher likelihood value. It is shown that exploitation of the closed-form solutions substantially improves the accuracy and efficiency of Monte Carlo simulations over high-order discretization algorithms. It is also shown that the feasibility of exact one-to-one calibration of the model to any continuous yield curve allows valuation of bond options significantly more accurately and efficiently.