Term Structure Models with Shot-Noise Effects

Abstract

This work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Gýrleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly.