Application of Vine Copulas to Credit Portfolio Risk Modeling

Marco Geidosch,Matthias Fischer

doi:10.3390/jrfm9020004

Marco Geidosch, Matthias Fischer

Open Access

https://doi.org/10.3390/jrfm9020004

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Abstract

In this paper, we demonstrate the superiority of vine copulas over conventional copulas when modeling the dependence structure of a credit portfolio. We show statistical and economic implications of replacing conventional copulas by vine copulas for a subportfolio of the Euro Stoxx 50 and the S&P 500 companies, respectively. Our study includes D-vines and R-vines where the bivariate building blocks are chosen from the Gaussian, the t and the Clayton family. Our findings are (i) the conventional Gauss copula is deficient in modeling the dependence structure of a credit portfolio and economic capital is seriously underestimated; (ii) D-vine structures offer a better statistical fit to the data than classical copulas, but underestimate economic capital compared to R-vines; (iii) when mixing different copula families in an R-vine structure, the best statistical fit to the data can be achieved which corresponds to the most reliable estimate for economic capital.

Highlights

From a methodological viewpoint, a misconception of credit portfolio risk was a core reason for the financial crisis of 2007–2008 (In particular, valuation of credit debt obligations (CDOs) is to a large extent based on measuring the credit portfolio risk of the underlying pool of loans
Against the background of this criticism, we introduce vine copulas to the field of credit portfolio risk modeling and show that vine copulas are superior to conventional copulas
Compared to their traditional counterparts, D-vine copulas result in remarkably lower economic capital values, which holds for both portfolios (e.g., Euro Stoxx and Clayton: 29.1 vs. 16.7)

Summary

Introduction

A misconception of credit portfolio risk was a core reason for the financial crisis of 2007–2008 (In particular, valuation of credit debt obligations (CDOs) is to a large extent based on measuring the credit portfolio risk of the underlying pool of loans. Modeling the correlation structure of a credit portfolio is mainly based on the Gaussian copula, which has received much criticism even in a non-academic context, see [4]. There are numerous bivariate copula families with different properties that serve as building blocks for vine copulas, see [5,6] This variety of bivariate copulas is exploited to form a rich and powerful multivariate distribution class even in large dimensions, which can model asymmetric and complex dependence structures. The dependence structure of the portfolio, which is the main concern of this paper, is modeled with copula functions. Many banks rely on equity data for the calibration of the dependence structure of their internal credit portfolio models.

A Short Primer on Pair-Copulas Including Specification and Estimation

Calculating Economic Capital Based on Copulas

Simulation Experiments

Applying Vine Copulas to a Credit Portfolio

Findings

Conclusions