Extreme value theory evt yields methods for quantifying such events and their consequences in a statistically optimal way. In evt the focus of interest is the so called tail index that characterizes the shape of the. Extreme value theory and statistics for heavy tail data. One of the possible approaches is to use the extreme value theory evt. The right tail of the daily loss distribution is heavy. Section 6 reports the results of a small simulation study to validate the practical. 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. Exponentialgeneralized pareto distribution, is characterized by its pdf h ex pressed as. 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. Extreme value modelling of the ghana stock exchange index. Extreme value theory is considered to provide the basis for the statistical. Extreme expectile estimation for heavytailed time series.
Operator extreme value theory 409 can be treated with scalar norming, with the same tail index in every radial direction. The cdf of the generalized extreme value gev distribution satisfies. This index is directly related to the tail of a distribution function f with the tail function. 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.
The right tail of the daily loss distribution is heavy tailed with tail index from fe 5107 at national university of singapore. 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. Pdf extreme value theory for tailrelated risk measures. Apart from the probabilistic model, the other key component of a risk model is the measure of risk. Extreme value theory has been applied extensively in hydrology, climatology and also in the insurance industry. Exponential generalized pareto distribution, is characterized by its pdf h ex pressed as.