Modeling Credit Risk Contagion with Hawkes Process and its Application

Abstract

This article comprehensively reviews some applications of Hawkes process to credit risk modeling with “contagion effect”. Credit risk is the risk associated with financial losses caused by credit events such as debtorsʼ defaults or credit rating transitions. Financial institutions are required to assess more accurately total credit risk of their large credit portfolios for better risk managements. As such, credit risk quantification models are desired to capture the effect of credit risk contagions, which may cause extreme financial losses. Hawkes process is a nonnegative integer-valued stochastic process which has been often used as a basic model for counting contagious events such as infectious diseases in epidemiology and earthquake in seismology. Similarly, modeling with Hawkes process enables us to easily capture some features of contagious credit events and thus to improve the performance of assessing total credit risks. In addition, a multivariate Hawkes process has capability of estimating mutual contagion effects among different industrial sectors. In this article, as for credit risk modeling and analyses with Hawkes processes, not only an introductory theoretical review but some illustrative results from some recent works of the present authors of empirical analyses are presented.