A new copula class, Principal Component Copulas, merges copula-based methods with principal component models. It excels in modeling tail dependence in multivariate data by leveraging key directions. These copulas resemble factor copulas but exhibit distinct technicalities. They offer advantages in complex dependency modeling, especially in high dimensions, as demonstrated in simulations and applied to return data. Notably, they mitigate dimensionality issues in large models and excel in assessing tail risk, crucial for capital modeling.
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