On the Diversification Effect in Solvency II for Extremely Dependent Risks

Yongzhao Chen, Ka Chun Cheung, Sheung Chi Phillip Yam (), Fei Lung Yuen and Jia Zeng
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Yongzhao Chen: Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Siu Lek Yuen, Shatin, Hong Kong, China
Ka Chun Cheung: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong, China
Sheung Chi Phillip Yam: Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Fei Lung Yuen: School of Mathematics, Statistics and Actuarial Science, The University of Kent, Canterbury CT2 7NZ, UK
Jia Zeng: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong, China

Risks, 2023, vol. 11, issue 8, 1-22

Abstract: 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.

Keywords: diversification; extreme-value copula; spectral measure; Solvency II; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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