Non-extensive value-at-risk estimation during times of crisis

Ahmad Hajihasani (), Ali Namaki, Nazanin Asadi () and Reza Tehrani ()
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Ahmad Hajihasani: Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran
Ali Namaki: Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran
Nazanin Asadi: Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran
Reza Tehrani: Department of Finance, Faculty of Management, University of Tehran, Tehran, Iran

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 07, 1-11

Abstract: Value-at-risk (VaR) is a crucial subject that researchers and practitioners extensively use to measure and manage uncertainty in financial markets. Although VaR is a standard risk control instrument, there are criticisms about its performance. One of these cases, which has been studied in this research, is the VaR underestimation during times of crisis. In these periods, the non-Gaussian behavior of markets intensifies, and the estimated VaRs by typical models are lower than the real values. A potential approach that can be used to describe the non-Gaussian behavior of return series is the Tsallis entropy framework and nonextensive statistical methods. This paper has used the nonextensive models for analyzing financial markets’ behavior during crisis times. By applying the q-Gaussian probability density function for emerging and mature markets over 20 years, we can see a better VaR estimation than the regular models, especially during crisis times. We have shown that the q-Gaussian models composed of VaR and Expected Shortfall (ES) estimate risk better than the standard models. By comparing the ES, VaR, q-VaR and q-ES for emerging and mature markets, we see in confidence levels more than 0.98, the outputs of q models are more real, and the q-ES model has lower errors than the other ones. Also, it is evident that in the mature markets, the difference of VaR between normal condition and nonextensive approach increases more than one standard deviation during times of crisis. Still, in the emerging markets, we cannot see a specific pattern. The findings of this paper are useful for analyzing the risk of financial crises in different markets.

Keywords: Value-at-risk; non-extensive statistics; tsallis entropy; q-Gaussian distribution; complex systems (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0129183121500996

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