Abnormal Returns, Risk, and Options in Large Data Sets

Large data sets in finance with millions of observations have become widely available. Such data sets enable the construction of reliable semi-parametric estimates of the risk associated with extreme price movements. Our approach is based on semi-parametric statistical extreme value analysis, and compares favourably with the conventional finance normal distribution based approach. It is shown that the efficiency of the estimator of the extreme returns may benefit from high frequency data. Empirical tail shapes are calculated for the German Mark-US Dollar foreign exchange rate, and we use the semi- parametric tail estimates in combination with the empirical distribution function to evaluate the returns on exotic options.