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Heavy-tailed distributions in VaR calculations

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  • Adam Misiorek
  • Rafal Weron

Abstract

The essence of the Value-at-Risk (VaR) and Expected Shortfall (ES) computations is estimation of low quantiles in the portfolio return distributions. Hence, the performance of market risk measurement methods depends on the quality of distributional assumptions on the underlying risk factors. This chapter is intended as a guide to heavy-tailed models for VaR-type calculations. We first describe stable laws and their lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Next we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Then we discuss copulas, which enable us to construct a multivariate distribution function from the marginal (possibly different) distribution functions of n individual asset returns in a way that takes their dependence structure into account. This dependence structure may be no longer measured by correlation, but by other adequate functions like rank correlation, comonotonicity or tail dependence. Finally, we provide numerical examples.

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File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_10_05.pdf
File Function: Original version, 2010
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Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/10/05.

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Length: 38 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:wuu:wpaper:hsc1005

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Related research

Keywords: Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Parameter estimation; Value-at-Risk (VaR); Expected Shortfall (ES); Copula; Filtered historical simulation (FHS);

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References

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Cited by:
  1. Michele Leonardo Bianchi, 2014. "Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective," Temi di discussione (Economic working papers) 957, Bank of Italy, Economic Research and International Relations Area.

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