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Open AccessArticle

Probability of Default and Default Correlations

by Weiping Li 1,2
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
J. Risk Financial Manag. 2016, 9(3), 7; https://doi.org/10.3390/jrfm9030007
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)
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
MDPI and ACS Style

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

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