The limiting distribution of extremal exchange rate returns

Several nonnested fat‐tailed distributions have been advocated for modelling exchange rate returns. Instead of directly estimating these nonnested distributions we investigate the extremal distribution of the returns. The advantage is that the parameter which characterizes the amount of tail fatness can be estimated without maintaining a specific distribution, and hence enables one to test hypotheses. The parameter of the limit law is estimated by employing nonparametric procedures based on order statistics. The appropriateness of these procedures is assessed. Given this estimate one can derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of exchange rates.