A Markov Modulated Dynamic Contagion Process with Application to Credit Risk

Abstract

Self-exciting point processes are applied to various fields such as seismology, finance, neurophysiology, criminology, biology etc to model the clustering/contagion phenomenon and extreme risk events. This article proposes an analytically tractable point process, a generalization of the classical Hawkes process, with the intensity process following a Markov modulated mean-reverting affine jump-diffusion process with contagion effects. The proposed process has both self-exciting and externally-exciting jumps that represent the effects of endogenous and exogenous events. This article derives the closed-form expressions, for distributional properties such as the first order moment, probability generating function (PGF) of the point process and Laplace transform of the intensity process, which makes it computationally efficient. The application of the proposed process to price the synthetic collateralized debt obligations (CDOs) in a top-down framework is also presented.