A generalised contagion process with an application to credit risk

Angelos Dassios and Hongbiao Zhao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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. (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2017-02-01
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Citations: View citations in EconPapers (10)

Published in International Journal of Theoretical and Applied Finance, 1, February, 2017, 20(1). ISSN: 0219-0249

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