Survival Measures and Interacting Intensity Model: With applications in guaranteed debt pricing

by Qunfang Bao of the Zhejiang University,
Shenghong Li of the Zhejiang University, and
Guimei Liu of the Zhejiang University City College

December 25, 2010

Abstract: This paper studies survival measures in credit risk models. Survival measure, which was first introduced by Schönbucher [12] in the framework of defaultable LMM, has the advantage of eliminating default indicator variable directly from the expectation by absorbing it into Randon-Nikodym density process. Survival measure approach was further extended by Collin-Dufresne [4] to avoid calculating a troublesome jump in IBPR reduced-form model. This paper considers survival measure in "HBPR" model, i.e. default time is characterized by Cox construction, and studies the relevant drift changes and martingale representations. This paper also takes advantage of survival measure to solve the looping default problem in interacting intensity model with stochastic intensities. Guaranteed debt is priced under this model, as an application of survival measure and interacting intensity model. Detailed numerical analysis is performed in this paper to study influence of stochastic pre-default intensities and contagion on value of a two firms' bilateral guaranteed debt portfolio.

JEL Classification: G12, G13.

Keywords: Survival Measure, Interacting Intensity Model, Measure Change, Guaranteed Debt, Mitigation and Contagion

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