Steps in Applying Extreme Value Theory to Finance: A Review

Extreme value theory (EVT) has been applied in fields such as hydrology and insurance. It is a tool used to consider probabilities associated with extreme and thus rare events. EVT is useful in modelling the impact of crashes or situations of extreme stress on investor portfolios. Contrary to value-at-risk approaches, EVT is used to model the behaviour of maxima or minima in a series (the tail of the distribution). However, implementation of EVT faces many challenges, including the scarcity of extreme data, determining whether the series is "fat-tailed," choosing the threshold or beginning of the tail, and choosing the methods of estimating the parameters. This paper focuses on the univariate case; the approach is not easily extended to the multivariate case, because there is no concept of order in a multidimensional space and it is difficult to define the extremes in the multivariate case. Following a review of the theoretical literature, univariate EVT techniques are applied to a series of daily exchange rates of Canadian/U.S. dollars over a 5-year period (1995-2000).