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Adjusted empirical likelihood for value at risk and expected shortfall

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  • Zhen Yan
  • Junjian Zhang

Abstract

Value at risk (VaR) and expected shortfall (ES) are widely used risk measures of the risk of loss on a specific portfolio of financial assets. Adjusted empirical likelihood (AEL) is an important non parametric likelihood method which is developed from empirical likelihood (EL). It can overcome the limitation of convex hull problems in EL. In this paper, we use AEL method to estimate confidence region for VaR and ES. Theoretically, we find that AEL has the same large sample statistical properties as EL, and guarantees solution to the estimating equations in EL. In addition, simulation results indicate that the coverage probabilities of the new confidence regions are higher than that of the original EL with the same level. These results show that the AEL estimation for VaR and ES deserves to recommend for the real applications.

Suggested Citation

  • Zhen Yan & Junjian Zhang, 2017. "Adjusted empirical likelihood for value at risk and expected shortfall," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2580-2591, March.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:5:p:2580-2591
    DOI: 10.1080/03610926.2014.1002933
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