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Extreme Value Theory for Risk Managers
Alexander J. McNeil 
Departement Mathematik
ETH Zentrum

17th May 1999

Abstract
We provide an overview of the role of extreme value theory (EVT) in risk management
(RM), as a method for modelling and measuring extreme risks. We concentrate
on the peaks-over-threshold (POT) model and emphasize the generality of
this approach. Wherever the tail of a loss distribution is of interest, whether for
market, credit, operational or insurance risks, the POT method provides a simple
tool for estimating measures of tail risk. In particular we show how the POT method
may be embedded in a stochastic volatility framework to deliver useful estimates of
Value-at-Risk (VaR) and expected shortfall, a coherent alternative to the VaR, for
market risks. Further topics of interest, including multivariate extremes, models for
stress losses and software for EVT, are also discussed.