(a) Why is a member of the extreme value family of distributions usually more appropriate for capturing...

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(a) Why is a member of the extreme value family of distributions usually more appropriate for capturing tail behaviour than assuming normality for financial time-series?

(b) Explain the differences between the block maxima and peak over threshold frameworks for estimating the parameters of an extreme value distribution.

(c) What are the Weibull, Gumbel and Frechét distributions and which is the more appropriate for financial data?

(d) Outline the Hill and De Haan–Resnick approaches for estimating the parameters of extreme value distributions.

(e) What is the link between the tail index and the shape parameter for an extreme value distribution and what is the range of plausible values of the former?

(f) Explain how value at risk can be calculated using the delta normal method, historical simulation, and EVT. Compare and contrast the three approaches

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