Tail index extreme value theory pdf

Due to the power part, the tail of fx in the end always falls off more slowly than the tails of distributions such as the normal and lognormal, which have exponential like tails. Exponential generalized pareto distribution, is characterized by its pdf h ex pressed as. Most financial data appear to be heavy tailed in this sense. Extreme value theory and statistics for heavy tail data. Pdf extreme value theory for tailrelated risk measures. This index is directly related to the tail of a distribution function f with the tail function. Beirlant, g matthys, g dierckx, heavy tailed distributions and rating,astin bulletin, vol 31, no 1, pp 37 58, may 2001 comprehensive list of references patrik p and guiahi f, an extrememly important application of extreme value theory to reinsurance pricing. Extreme value modelling of the ghana stock exchange index. The right tail of the daily loss distribution is heavy. Arguably the bestknown quantilebased risk measure in banking, and the nancial sector generally, is value atrisk. Extreme value theory has been applied extensively in hydrology, climatology and also in the insurance industry. Extreme value theory and statistics for heavy tail data repub. Extreme expectile estimation for heavytailed time series.

Apart from the probabilistic model, the other key component of a risk model is the measure of risk. Exponentialgeneralized pareto distribution, is characterized by its pdf h ex pressed as. Extreme value theory evt yields methods for quantifying such events and their consequences in a statistically optimal way. Pdf of the standard extreme value distributions for. We start with a visual analysis of market index returns, to emphasize the frequent occurrence of large market swings. The generalized extreme value gev distribution, implied. The cdf of the generalized extreme value gev distribution satisfies. Extreme value theory is considered to provide the basis for the statistical.

Extreme v alue theory for risk managers alexander j. Chapter 4 extreme value theory 1 motivation and basics the risk management is naturally focused on modelling of the tail events low probability, large impact. For a general equity book, for instance, a risk manager will be interested. See mcneil 1998 for an interesting discussion of the 1987 crash example. The right tail of the daily loss distribution is heavy tailed with tail index from fe 5107 at national university of singapore. One of the possible approaches is to use the extreme value theory evt. An application of extreme value theory for measuring financial. In evt the focus of interest is the so called tail index that characterizes the shape of the. Extreme value theory is a robust framework to analyse the tail behaviour of distributions. This paper models the extreme values of the ghana stock exchange allshares index 20002010 by applying the extreme value theory evt to fit a model to the tails of the daily stock returns data.