Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

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• 作者：M. Kratz (1)
  
• 关键词：Aggregated risk ; (refined) Berry ; Ess茅en inequality ; (generalized) Central limit theorem ; Conditional (Pareto) distribution ; Conditional (Pareto) moment ; Convolution ; Expected shortfall ; Extreme values ; Extreme quantiles ; Financial data ; Heavy tail ; High frequency data ; Market risk ; Order statistics ; Pareto distribution ; Rate of convergence ; Risk measures ; Stable distribution ; Sum of iid random variables ; Value ; at ; risk ; Primary鈥?0F05 ; 62G32 ; 62G30 ; 62P05 ; Secondary鈥?2G20 ; 91B30 ; 91G70
• 刊名：Extremes
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：17
• 期：4
• 页码：661-691
• 全文大小：1,363 KB
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• 作者单位：M. Kratz (1)
  
  1. ESSEC Business School, CREAR Risk Research Center, Avenue Bernard Hirsch BP 50105, 95021, Cergy-Pontoise Cedex, France
  
• ISSN：1572-915X

文摘

We develop theoretically as well as numerically a new method, Normex, for the sum of independent heavy tailed distributed random variables, to obtain the most accurate evaluation of its entire distribution. Normex provides sharp results, whatever the number of summands and the tail index are. It is particularly suited when the Central Limit Theorem (CLT) applies but with slow convergence of the mean and with a poor approximation for the tail. Hence, it is filling up a gap in the literature by giving an appropriate limit distribution in this case, in general better than with most standard methods. An application is developed to evaluate the Value-at-Risk of the yearly log returns of financial assets.