Skip to main content

2013 | OriginalPaper | Buchkapitel

Vulnerability of Copula-VaR to Misspecification of Margins and Dependence Structure

verfasst von : Katarzyna Kuziak

Erschienen in: Algorithms from and for Nature and Life

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Copula functions as tools for modeling multivariate distributions are well known in theory of statistics and over the last decade have been gathering more and more popularity also in the field of finance. A Copula-based model of multivariate distribution includes both dependence structure and marginal distributions in such a way that the first may be analyzed separately from the later. Its main advantage is an elasticity allowing to merge margins of one type with a copula function of another one, or even bound margins of various types by a common copula into a single multivariate distribution. In this article copula functions are used to estimate Value at Risk (VaR). The goal is to investigate how misspecification of marginal distributions and dependence structure affects VaR. As dependence structure normal and student-t copula are considered. The analysis is based on simulation studies.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
Tool: Matlab ver. 7.9.0.529 (2009b).
 
Literatur
Zurück zum Zitat Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. New York: Wiley.MATHCrossRef Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. New York: Wiley.MATHCrossRef
Zurück zum Zitat Crouhy, M., Galai, D., & Mark, R. (2001). Risk Management. New York: McGraw-Hill. Crouhy, M., Galai, D., & Mark, R. (2001). Risk Management. New York: McGraw-Hill.
Zurück zum Zitat Deheuvels, P. (1978). Caractérisation compléte des Luis Extrêmes Multivariées et de la Covergence des Types Extrêmes. Publications de l’Institut de Statistique de l’Université de Paris, 23(3), 1–36.MATH Deheuvels, P. (1978). Caractérisation compléte des Luis Extrêmes Multivariées et de la Covergence des Types Extrêmes. Publications de l’Institut de Statistique de l’Université de Paris, 23(3), 1–36.MATH
Zurück zum Zitat Deheuvels, P. (1981). A nonparametric test for independence. Publications de l’Institut de Statistique de l’Université de Paris, 26(2), 29–50.MathSciNetMATH Deheuvels, P. (1981). A nonparametric test for independence. Publications de l’Institut de Statistique de l’Université de Paris, 26(2), 29–50.MathSciNetMATH
Zurück zum Zitat Derman, E. (1996). Model risk. Risk, 9, 34–37. Derman, E. (1996). Model risk. Risk, 9, 34–37.
Zurück zum Zitat Embrechts, P., Hoing, A., & Juri, A. (2002). Using copulae to bound the Value-at-Risk for functions of dependent risks (Report), ETH Zurich. Embrechts, P., Hoing, A., & Juri, A. (2002). Using copulae to bound the Value-at-Risk for functions of dependent risks (Report), ETH Zurich.
Zurück zum Zitat Franke, J., Härdle, W. K., Hafner, Ch. M. (2011). Copulae and value at risk. In J. Franke, W. Härdle, & C. Hafner (Eds.), Statistics of financial markets. An introduction (pp. 405–446). Berlin/Heidelberg, Germany: Springer. Franke, J., Härdle, W. K., Hafner, Ch. M. (2011). Copulae and value at risk. In J. Franke, W. Härdle, & C. Hafner (Eds.), Statistics of financial markets. An introduction (pp. 405–446). Berlin/Heidelberg, Germany: Springer.
Zurück zum Zitat Genest, Ch., Quessy, J. F., & Remillard, B. (2006). Goodness-of-fit procedures for copula models based on the probability integral transformation. Scandinavian Journal of Statistics, 33(2), 337–366.MathSciNetMATHCrossRef Genest, Ch., Quessy, J. F., & Remillard, B. (2006). Goodness-of-fit procedures for copula models based on the probability integral transformation. Scandinavian Journal of Statistics, 33(2), 337–366.MathSciNetMATHCrossRef
Zurück zum Zitat Gregoriou, G., Hoppe, C., & Wehn, C. (2010). The risk modeling evaluation handbook: Rethinking financial risk management methodologies in the global capital markets. New York: McGraw-Hill. Gregoriou, G., Hoppe, C., & Wehn, C. (2010). The risk modeling evaluation handbook: Rethinking financial risk management methodologies in the global capital markets. New York: McGraw-Hill.
Zurück zum Zitat Hamerle, A., & Rösch, D. (2005). Misspecified copulas in credit risk models: How good is Gaussian? Journal of Risk, 8(1), 41–58. Hamerle, A., & Rösch, D. (2005). Misspecified copulas in credit risk models: How good is Gaussian? Journal of Risk, 8(1), 41–58.
Zurück zum Zitat Joe, H., & Xu, J. J. (1996). The estimation method of inference functions for margins for multivariate models (Tech. Rep. No. 166). Department of Statistics, University of British Columbia. Joe, H., & Xu, J. J. (1996). The estimation method of inference functions for margins for multivariate models (Tech. Rep. No. 166). Department of Statistics, University of British Columbia.
Zurück zum Zitat Kato, T., & Yoshiba, T. (2000). Model risk and its control (pp. 129–156). Tokyo: Monetary and Economic Studies. Kato, T., & Yoshiba, T. (2000). Model risk and its control (pp. 129–156). Tokyo: Monetary and Economic Studies.
Zurück zum Zitat Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer.MATH Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer.MATH
Zurück zum Zitat McNeil, A., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques, and tools. Princeton, NJ: Princeton University Press. McNeil, A., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques, and tools. Princeton, NJ: Princeton University Press.
Zurück zum Zitat Nelsen, R. (2006). An introduction to copulas (2nd ed.). New York: Springer.MATH Nelsen, R. (2006). An introduction to copulas (2nd ed.). New York: Springer.MATH
Zurück zum Zitat Weiss, G. N. F. (2011) Are Copula-GoF-tests of any practical use? Empirical evidence for stocks, commodities and FX futures. The Quarterly Review of Economics and Finance 51(2), 173–188.CrossRef Weiss, G. N. F. (2011) Are Copula-GoF-tests of any practical use? Empirical evidence for stocks, commodities and FX futures. The Quarterly Review of Economics and Finance 51(2), 173–188.CrossRef
Metadaten
Titel
Vulnerability of Copula-VaR to Misspecification of Margins and Dependence Structure
verfasst von
Katarzyna Kuziak
Copyright-Jahr
2013
DOI
https://doi.org/10.1007/978-3-319-00035-0_39