Quadratic Models for Portfolio Credit Risk with Shot-Noise Effects
by Raquel M. Gaspar of Stockholm School of Economics, and
Abstract: We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds.
Keywords: CDO, shot noise process, quadratic term structures, dependency, contagion.