On the Diversification Effect in Solvency II for Extremely Dependent Risks

In this article, we investigate the validity of diversification effect under extreme-value copulas, when the marginal risks of the portfolio are identically distributed, which can be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. We show that Value-a...

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Bibliographic Details
Published inRisks (Basel) Vol. 11; no. 8; p. 143
Main Authors Chen, Yongzhao, Cheung, Ka Chun, Yam, Sheung Chi Phillip, Yuen, Fei Lung, Zeng, Jia
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2023
Subjects
Diversification
extreme-value copula
Financial institutions
Random variables
Solvency
Solvency II
spectral measure
Value-at-Risk
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Summary:In this article, we investigate the validity of diversification effect under extreme-value copulas, when the marginal risks of the portfolio are identically distributed, which can be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. We show that Value-at-Risk (V@R) under extreme-value copulas is asymptotically subadditive for marginal risks with finite mean, while it is asymptotically superadditive for risks with infinite mean. Our major findings enrich and supplement the context of the second fundamental theorem of quantitative risk management in existing literature, which states that V@R of a portfolio is typically non-subadditive for non-elliptically distributed risk vectors. In particular, we now pin down when the V@R is super or subadditive depending on the heaviness of the marginal tail risk. According to our results, one can take advantages from the diversification effect for marginal risks with finite mean. This justifies the standard formula for calculating the capital requirement under Solvency II in which imperfect correlations are used for various risk exposures.
ISSN:2227-9091
2227-9091
DOI:10.3390/risks11080143