Extreme value theory and statistics for heavy tail data
January 2003
In Book
pp 169-178.
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A scientific way of looking beyond the worst-case return is to employ statistical extreme value methods. Extreme Value Theory (EVT) shows that the probability on very large losses is eventually governed by a simple function, regardless the specific distribution that underlies the return process. This limit result can be exploited to construct semi-parametric portfolio Value at Risk (VaR) estimates around and beyond the largest observed loss. Such extreme VaR estimates can be useful inputs for scenario analysis and stress testing. The aim of this chapter is to introduce the reader to extreme value theory and the statistics of extremes.
Keywords
Automatically Extracted Terms
- return
- distribution
- value
- tail index
- estimate
- value theory
- index
- function
- theory
- pareto
- density
- sample
- probability
- limit
- level
- hill estimator
- factor
- market
- risk management
- pareto factor
