A new copula for modeling portfolios with skewed, leptokurtic and high-order dependent risk factors

The paper proposes a new copula for modeling higher-order dependencies between pairs of portfolio assets, employing orthogonal polynomials to model symmetric co-kurtoses. Skewness and leptokurtosis of portfolio margins are modeled either with the Gram-Charlier expansion of the Normal distribution or Gram-Charlier-like expansions of leptokurtic laws. Details on the estimation method of this copula are provided, and a simulation study is carried out to assess its potential range of applicability with respect to widely employed alternatives in the copula literature. Empirical evidence of the suitability of this approach to model financial data and compute risk measures is provided.

Automated summary

The paper introduces a new copula for modeling higher-order dependencies between pairs of portfolio assets, utilizing orthogonal polynomials to model symmetric co-kurtoses. The method is shown to be suitable for modeling financial data and computing risk measures, with empirical evidence supporting its potential range of applicability in comparison to widely used alternatives in the copula literature.