A New Breed of Copulas for Risk and Portfolio Management

Abstract

We introduce the copula-marginal algorithm (CMA), a commercially viable technique to generate and manipulate a much wider variety of copulas than those commonly used by practitioners.

CMA consists of two steps: separation, to decompose arbitrary joint distributions into their copula and marginals; and combination, to glue arbitrary copulas and marginals into new joint distributions.

Unlike traditional copula techniques, CMA a) is not restricted to few parametric copulas such as elliptical or Archimedean; b) never requires the explicit computation of marginal cdf’s or quantile functions; c) does not assume equal probabilities for all the scenarios, and thus allows for advanced techniques such as importance sampling or entropy pooling; d) allows for arbitrary transformations of copulas. Furthermore, the implementation of CMA is also computationally very efficient in arbitrary large dimensions.

To illustrate benefits and applications of CMA, we propose two case studies: stress-testing with a panic copula which hits non-symmetrically the downside and displays non-equal, risk-premium adjusted probabilities; and arbitrary rotations of the panic copula.

Documented code for all the algorithms and the applications is available for download.

Keywords: panic copula, copula transformations, Archimedean, elliptical, Student t, non-parametric, scenarios-probabilities, empirical distribution, entropy pooling, importance sampling, grade, unit cube

JEL Classification: C1, G11