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Computing VAR and AVaR in Infinitely Divisible Distributions


Author Info

  • Young Kim
  • Svetlozar Rachev
  • Michele Bianchi
  • Frank Fabozzi


In this paper we derive closed-form solutions for the cumulative density 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.

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Bibliographic Info

Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number amz2569.

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Date of creation: 01 May 2009
Date of revision:
Handle: RePEc:ysm:somwrk:amz2569

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Keywords: tempered stable distribution; infinitely divisible distribution; value-at-risk; conditional value-at-risk; average value-at-risk;


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  1. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
  2. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1363-1378, July.
  3. O. E. Barndorff-Nielsen & S. Z. Levendorskii, 2001. "Feller processes of normal inverse Gaussian type," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 318-331.
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Cited by:
  1. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
  2. Alessandro Ramponi, 2012. "Computing Quantiles in Regime-Switching Jump-Diffusions with Application to Optimal Risk Management: a Fourier Transform Approach," Papers 1207.6759,
  3. Wylomanska-, Agnieszka, 2010. "Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution," MPRA Paper 28535, University Library of Munich, Germany, revised 2010.
  4. Joanna Janczura & Sebastian Orzel & Agnieszka Wylomanska, 2011. "Subordinated alpha-stable Ornstein-Uhlenbeck process as a tool for financial data description," HSC Research Reports HSC/11/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  5. Young Shin Kim & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2010. "Time series analysis for financial market meltdowns," Working Paper Series in Economics 2, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.


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