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A Dynamic Contagion Process and an Application to Credit Risk

1 Pages Posted: 15 Apr 2012  

Hongbiao Zhao

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); London School of Economics & Political Science (LSE)

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Date Written: May 24, 2011

Abstract

We introduce a new point process, the dynamic contagion process, by generalising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and exogenous factors of the underlying system. We have systematically analysed the theoretical distributional properties of this new process, based on the piece-wise deterministic Markov process theory developed by Davis (1984), and the extension of the martingale methodology used by Dassios and Jang (2003). The analytic expressions of the Laplace transform of the intensity process and the probability generating function of the point process have been derived. An explicit example of specified jumps with exponential distributions is also given. The object of this study is to produce a general mathematical framework for modelling the dependence structure of arriving events with dynamic contagion, which has the potential to be applicable to a variety of problems in economics, finance and insurance. We provide an application of this process to credit risk, and the simulation algorithm for further industrial implementation and statistical analysis.

Keywords: Dynamic contagion process, Cox process with shot noise intensity, piecewise-deterministic Markov process, cluster point process, self-exciting point process, Hawkes process

JEL Classification: C16

Suggested Citation

Zhao, Hongbiao and Dassios, Angelos, A Dynamic Contagion Process and an Application to Credit Risk (May 24, 2011). Available at SSRN: https://ssrn.com/abstract=2039798 or http://dx.doi.org/10.2139/ssrn.2039798

Hongbiao Zhao

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 361005
China

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

Angelos Dassios (Contact Author)

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

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