Computing VaR and AVaR in infinitely divisible distributions

  1. Young Shin Kim
  2. Svetlozar T. Rachev
  3. Michel Leonardo Bianchi
  4. Frank J. Fabozzi

Abstract

In this paper we derive closed-form solutions for the cumulative distribution function and the average value-at-risk for five subclasses of the infinitely divisible distributions: classical tempered stable distribution, Kim–Rachev distribution, modified tempered stable distribution, normal tempered stable distribution, and rapidly decreasing tempered stable distribution. We present empirical evidence using the daily performance of the S&P 500 for the period January 2, 1997 through December 29, 2006.
2000 AMS Mathematics Subject Classification: 60E07, 91B28.

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Probability and Mathematical Statistics

30, z. 2, 2010

Pages from 223 to 245

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