An application of extreme value theory in modelling extreme share returns

Extreme value theory (EVT) methods are used to investigate the asymptotic distri-bution/s of the extreme minima and maxima of the Athens Stock Exchange daily returns over the period 1976–2001. Innovative aspects of this study include: (1) the generalised extreme value and generalised logistic distributions are considered, (2) L-moments ratio diagrams are used to identify the distribution/s most likely to fit the extreme daily returns adequately, (3) the probability weighted moments method is used to estimate the parameters of the distribution/s, and (4) the Anderson–Darling goodness of fit test is employed to test the adequacy of fit. The generalised logistic distribution is found to provide adequate descriptions of the behaviour of both the extreme minima and maxima over the period studied; however, the asymptotic distributions of extremes appear to become less fat-tailed over time, implying that the probability of a large daily return occurring is decreasing.