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Expected shortfall estimation for apparently infinite-mean models of operational risk

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  • Pasquale Cirillo
  • Nassim Nicholas Taleb

Abstract

Statistical analyses on actual data depict operational risk as an extremely heavy-tailed phenomenon, able to generate losses so extreme as to suggest the use of infinite-mean models. But no loss can actually destroy more than the entire value of a bank or of a company, and this upper bound should be considered when dealing with tail-risk assessment. Introducing what we call the dual distribution, we show how to deal with heavy-tailed phenomena with a remote yet finite upper bound. We provide methods to compute relevant tail quantities such as the Expected Shortfall, which is not available under infinite-mean models, allowing adequate provisioning and capital allocation. This also permits a measurement of fragility. The main difference between our approach and a simple truncation is in the smoothness of the transformation between the original and the dual distribution. Our methodology is useful with apparently infinite-mean phenomena, as in the case of operational risk, but it can be applied in all those situations involving extreme fat tails and bounded support.

Suggested Citation

  • Pasquale Cirillo & Nassim Nicholas Taleb, 2016. "Expected shortfall estimation for apparently infinite-mean models of operational risk," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1485-1494, October.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:10:p:1485-1494
    DOI: 10.1080/14697688.2016.1162908
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    References listed on IDEAS

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    1. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
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    Cited by:

    1. Fontanari, Andrea & Cirillo, Pasquale & Oosterlee, Cornelis W., 2018. "From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 13-29.
    2. Taleb, Nassim Nicholas & Bar-Yam, Yaneer & Cirillo, Pasquale, 2022. "On single point forecasts for fat-tailed variables," International Journal of Forecasting, Elsevier, vol. 38(2), pages 413-422.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Nassim Nicholas Taleb & Yaneer Bar-Yam & Pasquale Cirillo, 2020. "On Single Point Forecasts for Fat-Tailed Variables," Papers 2007.16096, arXiv.org.
    5. Grobys, Klaus, 2023. "Correlation versus co-fractality: Evidence from foreign-exchange-rate variances," International Review of Financial Analysis, Elsevier, vol. 86(C).
    6. Di Lascio, F. Marta L. & Giammusso, Davide & Puccetti, Giovanni, 2018. "A clustering approach and a rule of thumb for risk aggregation," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 236-248.
    7. Martin Eling & Kwangmin Jung, 2022. "Heterogeneity in cyber loss severity and its impact on cyber risk measurement," Risk Management, Palgrave Macmillan, vol. 24(4), pages 273-297, December.
    8. Corral, Álvaro, 2024. "Moments of undersampled distributions: Application to the size of epidemics," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    9. Nassim Nicholas Taleb, 2016. "Stochastic Tail Exponent For Asymmetric Power Laws," Papers 1609.02369, arXiv.org, revised Apr 2017.
    10. Grobys, Klaus & Dufitinema, Josephine & Sapkota, Niranjan & Kolari, James W., 2022. "What’s the expected loss when Bitcoin is under cyberattack? A fractal process analysis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 77(C).

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