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

Email: ym{at}onetel.net.uk Empirical study of 25 years US Treasury bills data shows thateven when the spot interest rate remains fixed, its volatilityvaries significantly over time. Constant-coefficient modelscannot capture these changes as they give rise to time-homogeneousdistributions. Maximum likelihood fitting of a one-factor time-dependentExtended-CIR model of the term structure, whose closed-formsolution was previously obtained by the author, shows that itcan capture these changes, as well as achieve significantlyhigher likelihood value. It is shown that exploitation of theclosed-form solutions substantially improves the accuracy andefficiency of Monte Carlo simulations over high-order discretizationalgorithms. It is also shown that the feasibility of exact one-to-onecalibration of the model to any continuous yield curve allowsvaluation of bond options significantly more accurately andefficiently.