Credit risk with asymmetric information on the default threshold

Abstract

We study the impact of asymmetric information in a general credit model, where the default is triggered when a fundamental diffusion process of the firm passes below a random threshold. Inspired by some recent technical default events during the financial crisis, we consider the role of the firm's managers who choose the level of the default threshold and have complete information. However, other investors on the market only have partial observations either on the process or on the threshold. We specify the accessible information for different types of investors. Besides the framework of progressive enlargement of filtrations usually adopted in the credit risk modelling, we also combine the results on initial enlargement of filtrations to deal with the uncertainty on the default threshold. We consider several types of investors who have different information levels and we compute the default probabilities in each case. Numerical illustrations show that the insiders who have extra information on the default threshold obtain better estimations of the default probability than the standard market investors.

Keywords:

• credit risk
• insider
• enlargement of filtration

Acknowledgements

This research is part of the Chair Financial Risks of the Risk Foundation, the Chair Derivatives of the Future sponsored by the Fédération Bancaire Française, and the Chair Finance and Sustainable Development sponsored by EDF and Calyon.

Notes

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^1. In the classical reduced-form model such as the Cox-process model in Lando [18], X is an increasing process – the compensator process of default – instead of a decreasing one, and L is an upper bound. See §3.2 for details.

^2. In this example, the manager knows well the economic situation of the firm so that he has a good prior judgement on whether or not the terminal value of the firm will be greater or smaller than the constant threshold a.