Extreme Events and Extreme Value Theory (EVT) [23]

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Bullet points include: Type of limiting random variable to which extreme value converges is: Normal and log-normal tends to Gumbel. Student’s t tends to Fréchet. Uniform tends to Weibull. Weibull has an upper bound and is not generally used for tail risk purposes in a financial context. So if researcher believes normal distribution is not appropriate then generally focus on Fréchet, so in tail takes following form, for some alpha. pdf proportional to x^(-alpha-1). N.B. Link with generalised CLT and ‘stable’ distributions

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