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Abnormal returns, risk, and options in large data sets. (English) Zbl 0924.62108
Summary: Large data sets in finance with millions of observations have become widely available. Such data sets enable the construction of reliable semiparametric estimates of the risk associated with extreme price movements. Our approach is based on semiparametric statistical extreme value analysis, and compares favorably 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 semiparametric tail estimates in combination with the empirical distribution function to evaluate the returns on exotic options.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B28 Finance etc. (MSC2000)
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