A GENERALIZED CONTAGION PROCESS WITH AN APPLICATION TO CREDIT RISK

Angelos Dassios () and Hongbiao Zhao
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Angelos Dassios: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom
Hongbiao Zhao: Department of Finance, School of Economics and Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, P. R. China

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 01, 1-33

Abstract: We introduce a class of analytically tractable jump processes with contagion effects by generalizing 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, the Laplace transform of intensity process, and the 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 modeling 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 to 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (10)

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DOI: 10.1142/S0219024917500030

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