Probability equivalent level for CoVaR and VaR

Patricia Ortega-Jiménez, Franco Pellerey, Miguel Sordo and Alfonso Suárez-Llorens
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Patricia Ortega-Jiménez: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2024017, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: For a given risk, the well-known classical definition of Value-at-Risk (VaR) does not take into account possible interactions with other observable risks. For this reason, conditional VaRs that capture contagion effects and tail dependence among risks, such as the Co-Value-at-Risk (CoVaR), have been defined and studied in recent literature. In this paper we study conditions that guarantee, in the bivariate setting, the ordering between VaR and CoVaR, allowing to understand which, among the two measures, is more or less conservative than the other. By doing this, we introduce the notion of Probability Equivalent Level of CoVaR-VaR (PELCoV), which is the VaR value of the observable variable for which VaR and CoVaR coincide, and we study some of its properties such as uniqueness and boundedness. In particular, we show that its properties are entirely explained by the copula that describes the dependence between risks, and we provide a list of copulas for which PELCoV is explicitly available, and for which it is or not bounded. A practical applicative example is also presented.

Keywords: Systematic risk; Contagion risk measure; Value at risk; Conditional value at risk; Stochastically increasing (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Pages: 14
Date: 2024-01-10
Note: In: Insurance Mathematics and Economics, 2024, vol. 115, p. 22-35
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024017

DOI: 10.1016/j.insmatheco.2023.12.004

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