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

TL;DR

This paper empirically evaluates multi-factor Gaussian models for pricing Italian sovereign bonds, focusing on calibration techniques over a 12-year period including financial crises.

Contribution

It provides an empirical assessment of Cox-Ingersoll-Ross and Vasicek models for Italian BTPs using advanced calibration methods like Kalman filtering.

Findings

Multi-factor Gaussian models can be calibrated effectively to Italian BTP data.

The paper offers analytic formulas for likelihood function derivatives, enhancing calibration accuracy.

Models capture bond price dynamics during financial crises.

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 12-year horizon, including the global financial crisis and the euro area sovereign debt crisis. Analytic formulas for the gradient vector and the Hessian matrix of the likelihood function are provided.