Int. J. of Intelligent Engineering Informatics   »   2011 Vol.1, No.2

 

 

Title: A Markovian infectious model for dependent default risk

 

Author: Jia-Wen Gu, Wai-Ki Ching, Tak-Kuen Siu

 

Addresses:
Department of Mathematics, Advanced Modelling and Applied Computing Laboratory, The University of Hong Kong, Pokfulam Road, Hong Kong.
Department of Mathematics, Advanced Modelling and Applied Computing Laboratory, The University of Hong Kong, Pokfulam Road, Hong Kong.
Department of Actuarial Studies and Centre of Financial Risk, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia

 

Abstract: Modelling dependent defaults has long been a central issue for credit risk measurement and management. To address this important issue, we introduce a Markovian infectious model to describe the dependent relationship of default processes of credit securities. The central tenant of the proposed model is the concept of common shocks which is one of the major approaches to describe insurance risk. Using real data default data, we compare the proposed model to some existing default risk models, such as one-sector and two-sector models discussed in Ching et al. (2008, 2010). A log likelihood ratio test is adopted for the purpose of model comparison. Our empirical results reveal that the proposed model outperforms both the one-sector and two-sector models. We also illustrate the application of the proposed model for quantitative risk measurement. In particular, numerical results for both the crisis value-at-risk and the crisis expected shortfall are provided.

 

Keywords: dependent default risk; Markovian infectious models; common shocks; multi-sector modelling; chain reaction; crisis risk measures; credit risk management; default processes; credit securities; insurance risk; value-at-risk; expected shortfall.

 

DOI: 10.1504/IJIEI.2011.040178

 

Int. J. of Intelligent Engineering Informatics, 2011 Vol.1, No.2, pp.174 - 195

 

Available online: 19 May 2011

 

 

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