Measurement of Aggregate Risk with Copulas

By Markus Junker, A. May. 2005

149 citations recorded by the source corpus.

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. Copyright 2005 Royal Economic Society

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/bc2f77709e1533c717bfa5f842586d1aaf4ff099

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Citations in the corpus

Goodness-of-fit tests for copulas: A review and a power study (2006, background): “and Rivest (1993), Klugman and Parsa (1999), Andersen et al. (2005), Dobri´c and Schmid (2005) or Junker and May (2005) .”
Modeling and Generating Dependent Risk Processes for IRM and DFA (2004, background): “Mari and Kotz [20], p. 78; for recent applications in finance, see e.g. Junker and May [ 15 ].”
Copula-Based Approach to Accommodate Residential Self-Selection Effects in Travel Behavior Modeling (2009, methodology): “2005, Prieger, 2002, Zimmer and Trivedi, 2006, Cameron et al., 2004, Junker and May, 2005, and”
Testing Goodness of Fit for Parametric Families of Copulas—Application to Financial Data (2005, background): “Various authors have addressed this question (see e.g., Breymann et al., 2003; Fermanian, 2003; Junker and May, 2002; Malevergne and Sornette, 2003; Mashal and Zeevi, 2002; Savu and Trede, 2004).”
Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications (2006, unknown): “(1997): Multivariate Models and Dependence Concepts, Chapmann & Hall, London [24] Junker, M.”
An Overview of the Goodness-of-Fit Test Problem for Copulas (2012, methodology): “This idea of applying an arbitrary categorization of the data into contingency tables [0,1]d has been applied more or less fruitfully in a lot of papers: [46], [59], [33], [4], [58], etc.”
Simple Tests for Models of Dependence between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates (2004, methodology): “This model and variants of it have been used in Patton (2002a), Rockinger and Jondeau (2002), and Junker and May (2002), to name only a few.”
Estimating the tail-dependence coefficient: Properties and pitfalls (2005, unknown): “…the distribution function FG(x, y) = CG {Φ (x) , Φ (y) ; ϑ, δ} , where Φ denotes the univariate standard normal distribution and CG is an Archimedean copula with generator function φG(t ; ϑ, δ) = {φFrank(t ; ϑ)}δ = ( − log e −ϑt − 1 e−ϑ − 1 )δ , ϑ 6= 0, δ ≥ 1, considered by Junker and May (2002).”
Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification (2006, methodology): “In Junker and May (2002), the benchmark model is either the Student's t-copula or the Cook-Johnson copula.”
Test Statistics for Prospect and Markowitz Stochastic Dominances with Applications (2011, unknown): “…T A j (x) = ˆ F A j (x) − ˆ G A j (x) ˆ V A j (x) , (8) where ˆ V A j (x) = ˆ V A F j (x) + ˆ V A G j (x), 10 Dardanoni and Forcina (1999) and others have developed tests for Lorenz curve orderings, whereas Junker and May (2005) and others develop estimators to measure aggregate risk with copulas.”
Estimation and Model Selection of Copulas with an Application to Exchange Rates (2007, background): “…obviously the Value-at-Risk of a portfolio, as it might differ quite significantly when comparing its value under the assumption of joint normality and when having heavy tailed margins and a copula that allows for a higher dependence during market downturns (see for example Junker and May (2005).”