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Volume 40, Issue 1
Uncertainty Comparison Between Value-at-Risk and Expected Shortfall

Qing Liu, Weimin Liu, Liang Peng & Gengsheng Qin

DOI: 10.4208/cmr.2022-0071

Commun. Math. Res., 40 (2024), pp. 102-124.

Published online: 2023-12

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  • Abstract

Value-at-Risk (VaR) and expected shortfall (ES) are two key risk measures in financial risk management. Comparing these two measures has been a hot debate, and most discussions focus on risk measure properties. This paper uses independent data and autoregressive models with normal or $t$-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures. Theoretical and numerical analyses suggest that VaR at 99% level is better than ES at 97.5% level for distributions with heavier tails.

  • Keywords

$α$-mixing, asymptotic variance, expected shortfall, Value-at-Risk.

  • AMS Subject Headings

62P05, 62E20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-102, author = {Liu , QingLiu , WeiminPeng , Liang and Qin , Gengsheng}, title = {Uncertainty Comparison Between Value-at-Risk and Expected Shortfall}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {40}, number = {1}, pages = {102--124}, abstract = {

Value-at-Risk (VaR) and expected shortfall (ES) are two key risk measures in financial risk management. Comparing these two measures has been a hot debate, and most discussions focus on risk measure properties. This paper uses independent data and autoregressive models with normal or $t$-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures. Theoretical and numerical analyses suggest that VaR at 99% level is better than ES at 97.5% level for distributions with heavier tails.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0071}, url = {http://global-sci.org/intro/article_detail/cmr/22283.html} }
TY - JOUR T1 - Uncertainty Comparison Between Value-at-Risk and Expected Shortfall AU - Liu , Qing AU - Liu , Weimin AU - Peng , Liang AU - Qin , Gengsheng JO - Communications in Mathematical Research VL - 1 SP - 102 EP - 124 PY - 2023 DA - 2023/12 SN - 40 DO - http://doi.org/10.4208/cmr.2022-0071 UR - https://global-sci.org/intro/article_detail/cmr/22283.html KW - $α$-mixing, asymptotic variance, expected shortfall, Value-at-Risk. AB -

Value-at-Risk (VaR) and expected shortfall (ES) are two key risk measures in financial risk management. Comparing these two measures has been a hot debate, and most discussions focus on risk measure properties. This paper uses independent data and autoregressive models with normal or $t$-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures. Theoretical and numerical analyses suggest that VaR at 99% level is better than ES at 97.5% level for distributions with heavier tails.

Qing Liu, Weimin Liu, Liang Peng & Gengsheng Qin. (2023). Uncertainty Comparison Between Value-at-Risk and Expected Shortfall. Communications in Mathematical Research . 40 (1). 102-124. doi:10.4208/cmr.2022-0071
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