A comparison of some univariate models for Value-at-Risk and expected shortfall

Carlo Marinelli, Stefano D'Addona, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We compare in a backtesting study the performance of univariate models for Valueat-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum-stability assumption or the max-stability assumption, that respectively imply α-stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α-stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Original languageEnglish
Pages (from-to)1043-1075
Number of pages33
JournalInternational Journal of Theoretical and Applied Finance
Issue number6
StatePublished - Sep 2007


  • Expected shortfall
  • Extreme value theory
  • Paretian stable laws
  • Value-at-Risk


Dive into the research topics of 'A comparison of some univariate models for Value-at-Risk and expected shortfall'. Together they form a unique fingerprint.

Cite this