Measurement of aggregate risk with copulas

Angelika May

140 citations0/0 files storedEconometrics Journal

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Financial Risk and Volatility Modeling Risk and Portfolio Optimization Probability and Risk Models

Abstract

When aggregating financial risk on a portfolio level, the specification of the dependence structure between the risk factors plays an important role. Promising parametric models are often based on a so‐called copula approach. Case studies of market crashes suggest the application of concepts allowing for extremal dependence. We present a transformed copula as a new model that both fits the data and allows for exact prediction in the tails. It turns out that the new model improves benchmark models like the t‐ or Clayton copula with respect to risk measures like VaR or Expected Shortfall. By performing different goodness‐of‐fit tests, the quality of the estimation is examined.

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References

1999An Introduction to Copulas 2000Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach 1998Evaluating Density Forecasts with Applications to Financial Risk Management 1993Statistical Inference Procedures for Bivariate Archimedean Copulas 1995A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of Distributions 2003Modelling Dependence with Copulas and Applications to Risk Management 1988Bivariate Extreme Value Theory: Models and Estimation 2005Estimation of copula-based semiparametric time series models

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2011Statistical Tools for Finance and Insurance 2006A goodness of fit test for copulas based on Rosenblatt's transformation 2004Simple Tests for Models of Dependence between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates 2007Fully Nested 3-Copula: Procedure and Application on Hydrological Data 2013Copula Modelling of Dependence in Multivariate Time Series

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