Estimating Exposures to Tail Events

Michael Grimwade

“…these facts [the laws of probability] contribute a great deal to understanding, but hardly anything to practical [dice] play…”

Girolama Cardano, the earliest writer on probability, describing how his understanding of the laws of probability still did not help him win at dice!

The financial crisis of 2007–8 taught the industry and regulators both the importance of operational risk and the criticality of understanding firms’ exposures to the risks of suffering unexpected losses. In response, the industry and regulators have enhanced some existing risk-management techniques, such as scenario analysis and stress testing, and also developed a new technique, reverse stress testing. Although various regulatory bodies have published guidance, industry practices are still developing. Consequently, this chapter provides insights into how to undertake these risk-management activities more effectively, and also how they should link together. The definitions of these three risk-management techniques illustrate their similarities and differences.


    1. Scenario analysis – the assessment of the likelihood and impacts of specific operational risk events across a one-year time horizon.

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