Expected shortfall estimation for apparently infinite-mean models of operational risk. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Cirillo, Pasquale; Taleb, Nassim Nicholas
• Is Part Of: Quantitative finance. Volume 16:Issue 10(2016)
• Page Start: 1485
• Page End: 1494
• Publication Date: 2016-10-02
• Subjects: Value-at-risk -- Expected Shortfall -- Dual distribution -- Fat tails -- Upper bound -- Operational Risk -- Dismal Theorem; C13 -- C46 -- G32; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2016.1162908
• Languages: English
• ISSNs: 1469-7688

Abstract

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.