Intensity of default in sovereign bonds: Estimation of an unobservable process

This paper proposes a new approach to estimate general stationary diffusion processes that describe the evolution of unobserved arrival rates of credit events on sovereign bonds, allowing for arbitrary parametric drift and diffusion specifications. The solutions and transition processes for stationary diffusions are generally unknown in closed form and therefore standard maximum likelihood methods do not apply. Moreover, the arrival rates of credit events on sovereign bonds are unobservable and a direct nonparametric estimation does not work. This paper overcomes these challenges combining a semi-nonparametric estimator in the framework of the Efficient Method of Moments, Gallant and Tauchen (1996), and a reduced-form model for pricing sovereign bonds and credit default swaps. The application for Brazil sovereign assets explores the performance of the model under different specifications of the intensity process.