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Computing the Probability of a Financial Market Failure: A New Measure of Systemic Risk

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  • Robert Jarrow
  • Philip Protter
  • Alejandra Quintos

Abstract

This paper characterizes the probability of a market failure defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. The characterization employs a multivariate Cox process across the G-SIBs, which allows us to relate our work to the existing literature on intensity-based models. Various theorems related to market failure probabilities are derived, including the probability of a market failure due to two banks defaulting over the next infinitesimal interval, the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to 1.

Suggested Citation

  • Robert Jarrow & Philip Protter & Alejandra Quintos, 2021. "Computing the Probability of a Financial Market Failure: A New Measure of Systemic Risk," Papers 2110.10936, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2110.10936
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    References listed on IDEAS

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    1. Robert Engle, 2018. "Systemic Risk 10 Years Later," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 125-152, November.
    2. John Y. Campbell & Jens Hilscher & Jan Szilagyi, 2008. "In Search of Distress Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2899-2939, December.
    3. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Systemic Risk and Stability in Financial Networks," American Economic Review, American Economic Association, vol. 105(2), pages 564-608, February.
    4. Franklin Allen & Elena Carletti, 2013. "What Is Systemic Risk?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45, pages 121-127, August.
    5. Dimitrios Bisias & Mark Flood & Andrew W. Lo & Stavros Valavanis, 2012. "A Survey of Systemic Risk Analytics," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 255-296, October.
    6. Franklin Allen & Elena Carletti, 2013. "What Is Systemic Risk?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(s1), pages 121-127, August.
    7. Sudheer Chava & Robert A. Jarrow, 2008. "Bankruptcy Prediction with Industry Effects," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 21, pages 517-549, World Scientific Publishing Co. Pte. Ltd..
    8. Philip Protter & Alejandra Quintos, 2021. "Stopping Times Occurring Simultaneously," Papers 2111.09458, arXiv.org, revised Nov 2022.
    9. Sebastian Schich & Oana Toader, 2017. "To Be or Not to Be a G-SIB: Does It Matter?," Journal of Financial Management, Markets and Institutions, Società editrice il Mulino, issue 2, pages 169-192.
    10. Shumway, Tyler, 2001. "Forecasting Bankruptcy More Accurately: A Simple Hazard Model," The Journal of Business, University of Chicago Press, vol. 74(1), pages 101-124, January.
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    1. Philip Protter & Alejandra Quintos, 2021. "Stopping Times Occurring Simultaneously," Papers 2111.09458, arXiv.org, revised Nov 2022.

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