Abnormal Returns, Risk, and Options in Large Data Sets

Large data sets in finance with millions of observations have becomewidely available. Such data sets enable the construction of reliablesemi-parametric estimates of the risk associated with extreme pricemovements. Our approach is based on semi-parametric statisticalextreme value analysis, and compares favourably with the conventionalfinance normal distribution based approach. It is shown that theefficiency of the estimator of the extreme returns may benefit fromhigh frequency data. Empirical tail shapes are calculated for theGerman Mark-US Dollar foreign exchange rate, and we use the semi-parametric tail estimates in combination with the empiricaldistribution function to evaluate the returns on exotic options.