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Probability of Default and Default Correlations

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  • Weiping Li

    (Institute of Finance and Big Data, Southwest Jiaotong University, Chengdu 611756, Sichuan, China
    Department of Finance, Oklahoma State University, Stillwater, OK 74078-4011, USA)

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.

Suggested Citation

  • Weiping Li, 2016. "Probability of Default and Default Correlations," JRFM, MDPI, vol. 9(3), pages 1-19, July.
    • Handle: RePEc:gam:jjrfmx:v:9:y:2016:i:3:p:7-:d:73405
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    References listed on IDEAS

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    Cited by:

    1. Philip Protter & Alejandra Quintos, 2021. "Stopping Times Occurring Simultaneously," Papers 2111.09458, arXiv.org, revised Nov 2022.

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