Chapter 8. Extreme Value Theory

The risk of extreme losses is at the heart of many risk management problems both in insurance and finance. An extreme market move might represent a significant downside risk to the security portfolio of an investor. Reserves against future credit losses need to be sized to cover extreme loss scenarios in a loan portfolio. The required level of capital for a bank should be high enough to absorb extreme operational losses. Insurance companies need to be prepared for losses arising from natural or man-made catastrophes, even of a magnitude not experienced before.

Extreme Value Theory (EVT) is concerned with the statistical analysis of extreme events. The methodology provides distributions that are consistent with extreme observations and, at the same time, have parametric forms that are supported by theory. EVT's theoretical considerations compensate the unreliability of traditional estimates (caused by sparse data on extremes). EVT allows the quantification of...