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J. Risk Financial Manag. 2016, 9(3), 7; doi:10.3390/jrfm9030007

Probability of Default and Default Correlations

1
Institute of Finance and Big Data, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
2
Department of Finance, Oklahoma State University, Stillwater, OK 74078-4011, USA
Academic Editor: Jingzhi Huang
Received: 30 March 2016 / Revised: 31 May 2016 / Accepted: 23 June 2016 / Published: 5 July 2016
(This article belongs to the Special Issue Credit Risk)
View Full-Text   |   Download PDF [318 KB, uploaded 5 July 2016]

Abstract

We consider a system where the asset values of firms are correlated with the default thresholds. We first evaluate the probability of default of a single firm under the correlated assets assumptions. This extends Merton’s probability of default of a single firm under the independent asset values assumption. At any time, the distance-to-default for a single firm is derived in the system, and this distance-to-default should provide a different measure for credit rating with the correlated asset values into consideration. Then we derive a closed formula for the joint default probability and a general closed formula for the default correlation via the correlated multivariate process of the first-passage-time default correlation model. Our structural model encodes the sensitivities of default correlations with respect to the underlying correlation among firms’ asset values. We propose the disparate credit risk management from our result in contrast to the commonly used risk measurement methods considering default correlations into consideration. View Full-Text
Keywords: default correlation; probability of default; consistency; credit risk management; Kolmogorov forward equation; first-passage-time model; distance-to-default default correlation; probability of default; consistency; credit risk management; Kolmogorov forward equation; first-passage-time model; distance-to-default
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Li, W. Probability of Default and Default Correlations. J. Risk Financial Manag. 2016, 9, 7.

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