Affiliations: [a] Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong. E-mail: wching@hku.hk | [b] Hughes Hall, University of Cambridge, Wollaston Road, Cambridge, UK | [c] School of Economics and Management, Beijing University of Chemical Technology, North Third Ring Road, Beijing, China | [d] Department of Mathematics, Southern University of Science and Technology, Shenzhen, China. E-mail: jwgu.hku@gmail.com | [e] Department of Physics, National University of Defense Technology, Changsha, China. E-mail: lixiaoyuemxy@163.com | [f] Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia. E-mail: ken.siu@mq.edu.au | [g] Department of Mathematics, Imperial College, London, SW7 2AZ, UK. E-mail: h.zheng@imperial.ac.uk
Abstract: In this paper, we propose a general framework for modeling discrete-time default risk where default processes for all the entities are governed by predictable interacting default probabilities. We give a general formula for the joint distribution of two important random variables featuring the severity of the crisis: duration of a crisis (T) and severity of the defaults (WT). In particular, we present a two-sector Markovian infectious model, where the default probability is switching over time and depends on the current number of defaults of both sectors. The central idea of this model is that the causality of defaults of two sectors is in both directions, which enrich dynamics of the dependent default risk. The Bayesian Information Criterion (BIC) is adopted to compare the proposed model with the two-sector model in credit literature using real data. Numerical experiments are given to demonstrate that our proposed model is statistically better.
