The Distribution of Extremal Foreign Exchange Rate Returns in Extremely Large Data Sets

This study is based on an exceptionally large and automatically filtered data set containing most of the quoted prices on Reuters over 7 years. We employ semi-parametric extremal analysis. A bias reduction is attained by bootstrapping on resamples. The empirical results demonstrate the existence of the unconditional second moment of the distribution but the non-convergence of the fourth moment. Studies of cross-rates among European Monetary System currencies show a smaller tail index indicating a higher probability on extreme returns relative to the scale. The theory is subsequently applied to calculating the probabilities on as yet unseen extreme returns. This provides information to the treasurers of currency desks