Publication: Financial Dependence Analysis: Applications of Vine Copulae
Loading...
Files
Official URL
Full text at PDC
Publication Date
2013-01
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
This paper features the application of a novel and recently developed method of statistical and mathematical analysis to the assessment of financial risk: namely Regular Vine copulas. Dependence modeling using copulas is a popular tool in financial applications, but is usually applied to pairs of securities. Vine copulas offer greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which can be arranged and analysed in a tree structure to facilitate the analysis of multiple dependencies. We apply Regular Vine copula analysis to a sample of stocks comprising the Dow Jones Index to assess their interdependencies and to assess how their correlations change in different economic circumstances using three different sample periods: 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 there is evidence of greater reliance on the Student t copula in the copula choice within the tree structures for the GFC period, which is consistent with the existence of larger tails in the distributions of returns for this period. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co-dependencies.
Description
UCM subjects
Unesco subjects
Keywords
Citation
Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance, Mathematics and Economics, 44, 182-198.
Bedford, T. and R.M. Cooke (2001) Probability density decomposition for conditionally dependent random variables modeled by vines, Annals of Mathematics and Artificial 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. European Journal of Finance, 15, 675-701.
Berg, D. and Aas, K. (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 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 Valdesogo, A. (2009) Modeling international nancial returns with a multivariate regime switching copula. Journal of Financial Econometrics, 7, 437-480.
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 Scienti c 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.
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 , 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 Nikoloulopoulos, A. (2010) Tail dependence functions and vine copulas. Journal of Multivariate Analysis, 101(1), 252-270.
Kullback, S. and Leibler, R.A. (1951) On information and sufficiency. Annals of Mathematical Statistics, 22(1), 79-86.
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 Cooke R.M. (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(2), 193-213.
Min, A. and Czado, C. (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 Schirmacher, E. (2008) Multivariate dependence modeling using pair-copulas. Technical report, Society of Acturaries: 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., Czado, C., and Almeida, C. (2010) Modeling longitudinal data using a pair-copula decomposition of serial dependence. Under revision for Journal of the American Statistical Association.
Vuong, Q.H. (1989) Likelihood ratio tests for model selection and non-nested hypotheses . Econometrica, 57, 307-333.