Extended-Gaussian Term Structure Models and Credit Risk Applications

This paper presents three factor "Extended Gaussian" term struc- ture models (EGM) to price default-free and defaultable bonds. To price default-free bonds EGM assume that the instantaneous interest rate is a possibly non-linear but monotonic function of three latent factors that follow correlated Gaussian processes. The bond pricing equation can be solved conveniently through separation of variables and finite difference methods. The merits of EGM are hetero-schedastic yields, unrestricted correlation between factors and the absence of the admissibility restric- tions that affect canonical affine models. Unlike quadratic term structure models, EGM are amenable to maximum likelihood estimation, since ob- served yields are sufficient statistics to infer the latent factors. Empirical evidence from US Treasury yields shows that EGM fit observed yields quite well and are estimable. EGM are of even greater interest to price fixed and floating rate defaultable bonds. A reduced form, a credit rating based and a structural credit risk valuation model are presented: these credit risk models are EGM and their common merit is that bond pricing remains tractable through separation of variables even if interest rate risk and credit risk are arbitrarily correlated