Selecting copulas for risk management

Abstract

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student's t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.

Robust Estimation of Value-at-Risk through Distribution-Free and Parametric Approaches Using the Joint Severity and Frequency Model: Applications in Financial, Actuarial, and Natural Calamities Domains

“…Copulas have been used extensively in various applications in QRM (Nelsen 2007;Tewari et al 2011;Sklar 1959;Kojadinovic and Yan 2010;Panchenko 2005;Kojadinovic and Yan 2011;Kole et al 2007). In this paper, we propose to use the copula model in a generalized QRM setting where the losses are broken down in the joint severity/frequency model.…”

“…Gaussian copulas can model linear dependencies using the Pearson's correlation coefficient. The student's t-copula can capture dependencies in the tail region without sacrificing flexibility to model dependence in the body (Kole et al 2007). The GMCM offers more flexibility than the Gaussian copula, as the Gaussian copula is a special case (m = 1).…”

A Vine Copula Approach for Analyzing Financial Risk and Co-movement of the Indonesian, Philippine and Thailand Stock Markets

“…Furthermore, C-vine and Dvine copulas have been made use of in analyzing the conditional dependence for finance asset return, as they are more flexible than some multivariate copulas. For example, multivariate normal copula does not have tail dependence; multivariate t-copula has only a single degree of freedom parameter and symmetric tail dependence, while the nested Archimedian copulas and Hierarchical Archimedian copulas require additional parameter restrictions and thus result in reduced flexibility for modeling dependence structures (see Joe [15]; Savu and Trede [16]; Czado [22]). Various studies demonstrate the properties, classifications, structures, and merits of vine copulas (Nikoloulopoulos et al [5]; Kurowicka and Cooke [9]; Joe et al [10]; Joe [29]; Aas et al [23]).…”

“…Copulas have attracted much attention in the computation of value at risk, expected shortfall for risk measure, as pointed out by Kole et al [22], Junker and May [23], Ouyang et al [24], etc. In order to strengthen the practical applicability of the empirical results, we make use of the Monte Carlo simulation and the estimation results of the vine copula to calculate the VaR and ES of equally weighted portfolio.…”

Out-of-Sample Comparison of Copula Specifications in Multivariate Density Forecasts

“…Typically, one or several goodness-of-fit tests are applied to each of the competing specifications, and the copula that performs best on these statistics is selected; see Kole et al (2007) for an empirical example. A direct comparison of two alternative copulas has only been considered by and Patton (2006), adopting the approach based on pseudo likelihood ratio (PLR) tests for model selection originally developed by Vuong (1989) and Rivers and Vuong (2002).…”