Heavy-tailed distributions in VaR calculations

Adam Misiorek and Rafał Weron

No HSC/10/05, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

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.

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) (search for similar items in EconPapers)
JEL-codes: C13 C16 G32 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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