Publication: Risk Measurement and risk modelling using applications of Vine Copulas
Loading...
Files
Official URL
Full text at PDC
Publication Date
2014-05-06
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Citations
Exportar
Abstract
This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually applied to pairs of securities. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. The paper features the use of Regular Vine copulas in an analysis of the co-dependencies of 10 major European Stock Markets, as represented by individual market indices and the composite STOXX 50 index. The sample runs from 2005 to the end of 2011 to permit an exploration of how correlations change indifferent economic circumstances using three different sample periods: pre-GFC pre-GFC (Jan 2005- July 2007), GFC (July 2007-Sep 2009), and post-GFC periods (Sep 2009 - Dec 2011). The empirical results suggest that the dependencies change in a complex manner, and are subject to change in different economic circumstances. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co-dependencies. The practical application of Regular Vine metrics is demonstrated via an example of the calculation of the VaR of a portfolio made up of the indices.
Description
JEL Codes: G11, C02.
UCM subjects
Unesco subjects
Keywords
Citation
Aas, K., C. Czado, A. Frigessi and H. Bakken (2009) "Pair-copula constructions of multiple dependence", Insurance, Mathematics and Economics, 44, 182-198.
Allen, D. E., A. Ashraf, M. McAleer, R.J. Powell, and A.K. Singh, (2013) "Financial dependence analysis: applications of vine copulas", Statistica Neerlandica, 87, 4, 403-435.
Bedford, T. and R. M. Cooke (2001) "Probability density decomposition for conditionally dependent random variables modeled by vines", Annals of Mathematics and Articial Intelligence 32, 245-268.
Bedford, T. and R. M. Cooke (2002) "Vines - a new graphical model for dependent random variables", Annals of Statistics 30, 1031-1068.
Berg, D., (2009) "Copula goodness-of-fit testing: an overview and power comparison", The European Journal of Finance, 15:675-701.
Berg, D., and K. Aas, (2009) "Models for construction of higher-dimensional dependence: A comparison study", European Journal of Finance, 15:639-659.
Brechmann, E. C., C. Czado, and K. Aas, (2012) "Truncated regular vines and their applications", Canadian Journal of Statistics 40 (1), 68-85.
Brechmann, E.C. and C. Czado (2013), "Risk Management with High-Dimensional Vine Copulas: An Analysis of the Euro Stoxx 50", Statistics and Risk Modeling, 30(4), 307-342.
Brechmann, E.C., C. Czado and S. Paterlini (2014), "Flexible Dependence Modeling of Operational Risk Losses and Its Impact on Total Capital Requirements", Journal of Banking and Finance, 40, 271-285.
Brechmann, E.C., and U. Schepsmeier, (2012) "Modeling dependence with C- and D-vine copulas" The R-package CDVine, http://cran.rproject.org/web/packages/CDVine/vignettes/CDVine-package.pdf .
Brechmann, E. C., and C. Czado (2012) "COPAR - multivariate time-series modelling using the COPula AutoRegressive model", Working Paper, Faculty of Mathematics, Technical University of Munich.
Chollete, L., Heinen, A., and A. Valdesogo, (2009) "Modeling international financial returns with a multivariate regime switching copula", Journal of Financial Econometrics, 7:437-480.
Christoffersen, P., (1998) "Evaluating Interval Forecasts", International Economic Review, 39, 841-862.
Christoffersen, P., J. Hahn, and A. Inoue, (2001) "Testing and Comparing Value-at-Risk Measures", Journal of Empirical Finance, 8, 325-342.
Cooke, R.M., H. Joe and K. Aas, (2011) "Vines Arise", chapter 3 in DEPENDENCE MODELING Vine Copula Handbook, Ed. D. Kurowicka and H. Joe, World Scientific Publishing Co, Singapore.
Czado, C., U. Schepsmeier, and A. Min (2011) "Maximum likelihood estimation of mixed C-vines with application to exchange rates". To appear in Statistical Modelling.
Czado, C., E.C. Brechmann and L. Gruber (2013) "Selection of Vine Copulas", in P. Jaworski, F. Durante and W. K. Härdle (Eds.), Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012, Springer.
Dimann, J., E. C. Brechmann, C. Czado, and D. Kurowicka (2012) "Selecting and estimating regular vine copulae and application to financial returns", Submitted preprint. http://arxiv.org/abs/1202.2002.
Dissman, J.F. (2010) Statistical Inference for Regular Vines and Application, Thesis, Technische Universitat Munchen, Zentrum Mathematik.
Heinen, A. and A. Valdesogo (2009) "Asymmetric CAPM dependence for large dimensions: the canonical vine autoregressive model", CORE discussion papers 2009069, Universite catholique de Louvain, Center for Operations Research and Econometrics (CORE).
Joe, H., (1996) "Families of m-variate distributions with given margins and m(m- 1)/2 bivariate dependence parameters". In L. Rüschendorf and B. Schweizer and M. D. Taylor, editor, Distributions with Fixed Marginals and Related Topics.
Joe, H. (1997) Multivariate Models and Dependence Concepts. Chapman & Hall, London.
Joe, H., Li, H., and A. Nikoloulopoulos, (2010) "Tail dependence functions and vine copulas", Journal of Multivariate Analysis, 101(1):252-270.
Kullback, S. and R.A. Leibler, (1951) "On information and suficiency", The Annals of Mathematical Statistics, 22(1):79-86.
Kupiec, P., (1995) "Techniques for verifying the accuracy of risk measurement models", Journal of Derivatives 3, 73-84.
Kurowicka, D., (2011) "Optimal truncation of vines", In D. Kurowicka and H. Joe (Eds.), Dependence Modeling: Handbook on Vine Copulae. Singapore: World Scientific Publishing Co.
Kurowicka D. and R.M. Cooke, (2003) "A parametrization of positive definite matrices in terms of partial correlation vines", Linear Algebra and its Applications, 372, 225-251.
Kurowicka, D. and R. M. Cooke, (2006) "Uncertainty Analysis with High Dimensional Dependence Modelling", Chichester: John Wiley.
Mendes, B.V. d. M., M.M. Semeraro, and R. P. C. Leal, (2010) "Pair-copulas modeling in finance", Financial Markets and Portfolio Management 24, 193-213.
Min, A., and C. Czado, (2010) "Bayesian inference for multivariate copulas using pair-copula constructions", Accepted for publication in Journal of Financial Econometrics.
Morales-N´apoles, O., R. Cooke, and D. Kurowicka (2009) "About the number of vines and regular vines on n nodes", Submitted to Linear Algebra and its Applications.
Nelsen, R., (2006) An Introduction to Copulas, Springer, New York, 2nd edition.
Patton, A. J., (2009) "Copula based models for financial time series", in: Handbook of Financial Time Series. pp. 767-785.
Prim, R. C., (1957) ·Shortest connection networks and some generalizations", Bell System Technical Journal, 36:1389-1401.
Schirmacher, D. and E. Schirmacher, (2008) "Multivariate dependence modeling using pair-copulas", Technical report, Society of Actuaries: 2008 Enterprise Risk Management Symposium, April 14-16, Chicago. Available from: http://www.soa.org/library/monographs/other-monographs/2008/april/ 2008-ermtoc.aspx .
Sklar, A., (1959) "Fonctions de repartition a n dimensions et leurs marges", Publications de l'Institut de Statistique de L'Universite de Paris 8, 229-231.
Smith, M., Min, A., C. Czado, C., and C. Almeida, (2010) "Modeling longitudinal data using a pair-copula decomposition of serial dependence", In revision for the Journal of the American Statistical Association.
Vuong, Q. H., (1989) "Likelihood ratio tests for model selection and non-nested hypotheses", Econometrica, 57:307-333.