Asymptotic behavior of systemic risk based on the higher-moment capital allocation

Jiangyan Peng; Maojie Ye; Chenghao Xu

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This paper investigates the asymptotic behavior of systemic expected shortfall and marginal expected shortfall under conditions of both asymptotic dependence and independence, within a framework where capital allocation is guided by the higher moment risk measure.
This paper derives the asymptotic expressions for SES and MES under the assumptions of multivariate regular variation and pairwise quasi-asymptotic independence.
Our results establish that the systemic risk is asymptotically proportional to value-at risk.
A detailed numerical simulation study to validate and analyze the parameters from various perspectives is presented, while we also outline the computational procedures and methodologies employed.

Abstract

For a static model of n individuals generated by heavy-tailed losses, under the assumption that there exist asymptotic independence and dependence structures between the losses, we derive asymptotic formulas for both the systemic expected shortfall and marginal expected shortfall based on higher-moment capital allocation rules. Our results indicate that systemic risk is asymptotically proportional to the value-at-risk of a representative random variable, and it is influenced by the risk aversion parameter p and the structure of asymptotic dependence, while the structure of asymptotic independence has a negligible effect. In addition, simulation studies are conducted to better illustrate our results.

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