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The economic default time and the arcsine law

Author

Listed:
  • Xin Guo

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720-1777, USA)

  • Robert A. Jarrow

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853, USA;
    Kamkura Corporation, USA)

  • Adrien de Larrard

    (Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, 175, rue du Chevaleret, 75013 Paris, France)

Abstract

This paper proposes a new mathematical notion of "economic default" and 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 recorded default time. This work is motivated by the empirical study of Guo et al. (2008) which supports the distinction between the two default times. The probability distribution for the time span between economic and recorded defaults is analyzed, and is shown to follow a mixture of arcsine laws when the firm's asset value process is modeled by a geometric Brownian motion.

Suggested Citation

  • Xin Guo & Robert A. Jarrow & Adrien de Larrard, 2014. "The economic default time and the arcsine law," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-18.
    • Handle: RePEc:wsi:jfexxx:v:01:y:2014:i:03:n:s2345768614500251
    DOI: 10.1142/S2345768614500251
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Kim, Sung Ik, 2023. "A comparative study of firm value models: Default risk of corporate bonds," Finance Research Letters, Elsevier, vol. 56(C).

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