Are multi-factor Gaussian term structure models still useful? An empirical analysis on Italian BTPs

Abstract

In this paper, we empirically study models for pricing Italian sovereign bonds under a reduced form framework, by assuming different dynamics for the short-rate process. We analyze classical Cox-Ingersoll-Ross and Vasicek multi-factor models, with a focus on optimization algorithms applied in the calibration exercise. The Kalman filter algorithm together with a maximum likelihood estimation method are considered to fit the Italian term-structure over a 17-year horizon, including the global financial crisis, the euro area sovereign debt crisis and the Italian political turmoil in 2018. Analytic formulas for the gradient vector and the Hessian matrix of the likelihood function are provided.