Order Statistics and Their Applications to Quantitative Finance

概要

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This study concerns about order statistics and their applications to quantitative finance. So far, theories and applications of order statistics have been well developed and applied to many scientific fields ranging from conventional statistical problems to recent biostatistical researches. It has been shown that order statistics have many good statistical properties which other ones don't deserve. In this study, firstly some statistical properties and results of order statistics are reviewed and summarized. Secondly, applications of order statistics in quantitative finance, such as, valuation of the VaR (Value At Risk), estimation of tail distributions of financial assets etc., are to be discussed. Through these applications, it is shown that order statistics also play an important role in analyzing the extreme values (minima and maxima) in financial markets. Here, we not only utilize order statistics to analyze the extreme values, but also consider the ranges distribution (difference between any two order statistics of asset prices), especially the possibilities of applications of the ranges distribution to risk management.
久留米大学の論文