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Conditional generalized quantiles as systemic risk measures: Properties, estimation, and application

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  • Hakim, Arief
  • Salman, A.N.M.
  • Syuhada, Khreshna

Abstract

The conditional L1-quantile, or simply conditional quantile, is vital for measuring systemic risk, i.e., the risk that the distress experienced by one or more financial markets spreads to the others. One may formulate conditional quantile-based value-at-risk (CoVaR), but it depends only on the probability of loss occurrence. Alternatively, one may define conditional expectile-based value-at-risk (CoEVaR) or L2-CoVaR, but it is too sensitive and thus unrobust to extreme losses. In this paper, we aim to construct a generalized measure of systemic risk, called Lp-CoVaR, based on conditional Lp-quantiles when the conditioning risks are measured using Lp-VaR, where p≥1. We find that the Lp-VaR and Lp-CoVaR are coherent for all linear portfolios of elliptically distributed losses and are asymptotically coherent at high confidence level for independently and identically distributed losses with heavy right-tail. In addition, we determine their estimators and the respective asymptotic properties. In particular, we perform the Lp-CoVaR estimation using multivariate copulas, enabling us to link marginal risk models and capture their complex dependence. Our Monte Carlo simulation study demonstrates that the Lp-VaR and Lp-CoVaR estimators with 1

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  • Hakim, Arief & Salman, A.N.M. & Syuhada, Khreshna, 2025. "Conditional generalized quantiles as systemic risk measures: Properties, estimation, and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 235(C), pages 60-84.
    • Handle: RePEc:eee:matcom:v:235:y:2025:i:c:p:60-84
    DOI: 10.1016/j.matcom.2025.03.011
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