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The economic default time and the Arcsine law

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  • Xin Guo
  • Robert A Jarrow
  • Adrien de Larrard

Abstract

This paper develops a structural credit risk model to characterize the difference between the economic and recorded default times for a firm. Recorded default occurs when default is recorded in the legal system. The economic default time is the last time when the firm is able to pay off its debt prior to the legal default time. It has been empirically documented that these two times are distinct (see Guo, Jarrow, and Lin (2008)). In our model, the probability distribution for the time span between economic and recorded defaults follows a mixture of Arcsine Laws, which is consistent with the results contained in Guo, Jarrow, and Lin. In addition, we show that the classical structural model is a limiting case of our model as the time period between debt repayment dates goes to zero. As a corollary, we show how the firm value process's parameters can be estimated using the tail index and correlation structure of the firm's return.

Suggested Citation

  • Xin Guo & Robert A Jarrow & Adrien de Larrard, 2010. "The economic default time and the Arcsine law," Papers 1012.0843, arXiv.org, revised Jan 2011.
    • Handle: RePEc:arx:papers:1012.0843
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    Cited by:

    1. Jia-Wen Gu & Bo Jiang & Wai-Ki Ching & Harry Zheng, 2016. "On Modeling Economic Default Time: A Reduced-Form Model Approach," Computational Economics, Springer;Society for Computational Economics, vol. 47(2), pages 157-177, February.
    2. Kim, Sung Ik, 2023. "A comparative study of firm value models: Default risk of corporate bonds," Finance Research Letters, Elsevier, vol. 56(C).
    3. Jiang, Jia-Jian & He, Ping & Fang, Kai-Tai, 2015. "An interesting property of the arcsine distribution and its applications," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 88-95.
    4. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.

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