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A New Breed of Copulas for Risk and Portfolio Management

Attilio Meucci

ARPM - Advanced Risk and Portfolio Management

May 22, 2011

Risk, Vol. 24, No. 9, pp. 122-126, 2011

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.

Number of Pages in PDF File: 17

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

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Date posted: May 13, 2011 ; Last revised: August 28, 2011

Suggested Citation

Meucci, Attilio, A New Breed of Copulas for Risk and Portfolio Management (May 22, 2011). Risk, Vol. 24, No. 9, pp. 122-126, 2011. Available at SSRN: https://ssrn.com/abstract=1752702

Contact Information

Attilio Meucci (Contact Author)
ARPM - Advanced Risk and Portfolio Management ( email )
HOME PAGE: http://www.arpm.co/
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