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MODELING PORTFOLIO LOSS DEPENDENCE USING FRÉCHET DISTRIBUTION AND NESTED CLAYTON COPULAS
Keywords:
Fréchet distribution, Archimedean copula, hierarchical copulas, Value at Risk, extreme values, default timeDOI:
https://doi.org/10.17654/0972086325023Abstract
In modern financial analysis, stochastic models are increasingly used to assess potential outcomes in risky environments. This paper proposes an approach to modeling the dependence of losses within a large portfolio, using the Fréchet distribution to describe the stochastic behavior of default times and a three-level nested Archimedean copula of the Clayton type to model the maximum value of the Value at Risk (VaR). The portfolio is subdivided into sectors and subsectors, allowing for an analysis of risk propagation among different groups of assets. Our results show that the maximum VaR is an increasing function of certain parameters of the Fréchet distribution and that the hierarchical structure of the Clayton copulas provides a flexible framework for modeling multivariate dependence.
Received: October 22, 2025
Accepted: November 26, 2025
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