A Generalised Contagion Process with an Application to Credit Risk

35 Pages Posted: 6 Dec 2016 Last revised: 11 May 2022

See all articles by Angelos Dassios

Angelos Dassios

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

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Date Written: December 6, 2016

Abstract

We introduce a class of analytically tractable jump processes with contagion effects by generalising the classical Hawkes process. This model framework combines the characteristics of three popular point processes in the literature:

(1) Cox process with CIR intensity;

(2) Cox process with Poisson shot-noise intensity;

(3) Hawkes process with exponentially decaying intensity.

Hence, it can be considered as a self-exciting and externally-exciting point process with mean-reverting stochastic intensity. Essential probabilistic properties such as moments, Laplace transform of intensity process, and probability generating function of point process as well as some important asymptotics have been derived. Some special cases and a method for change of measure are discussed. This point process may be applicable to modelling contagious arrivals of events for various circumstances (such as jumps, transactions, losses, defaults, catastrophes) in finance, insurance and economics with both endogenous and exogenous risk factors within one framework. More specifically, these exogenous factors could contain relatively short-lived shocks and long-lasting risk drivers. We make a simple application to calculate the default probability for credit risk and price defaultable zero-coupon bonds.

Keywords: Credit risk, Contagion risk, Stochastic intensity model, Jump process, Point process, Self-exciting process, Hawkes process, Cox process, CIR process, Dynamic contagion process, Dynamic contagion process with diffusion

JEL Classification: C02, G13

Suggested Citation

Dassios, Angelos and Zhao, Hongbiao, A Generalised Contagion Process with an Application to Credit Risk (December 6, 2016). International Journal of Theoretical and Applied Finance, Available at SSRN: https://ssrn.com/abstract=2881217

Angelos Dassios

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

Houghton Street
London, England WC2A 2AE
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

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