Simple Time-Varying Copula Estimation
Treść / Zawartość
This article examines the ability of time-varying Gaussian and Student / copulas to accurately predict the probability of joint extreme co-movements in stock index returns. Using a sample of more than 20 years of daily return observations of the Eurostoxx 50 and Dow Jones Industrial 30 stock indices, Gaussian and Student / copulas are calibrated daily on a rolling window of the 250 most recent observations. We do not make assumptions on the functional form of the marginal distributions. Thus, the focus remains on the examination of the appropriateness of the two types of copulas. One of our findings is that there are time periods when the assumption of a Gaussian copula seems to be accurate and when the hypothesis of a Gaussian copula cannot be rejected in favor of a Student t copula. In other time periods, the hypothesis of a Gaussian copula can be rejected, as it underestimates the probability of joint extreme co-movements. This time periods of joint extreme co-movements are typically associated with a higher volatility environment and higher correlations between stock index returns. In applying a hit test to examine the ability of both copulas to predict the probability of joint strongly negative returns of both indices, we reject the null hypothesis of a Gaussian copula while the null hypothesis of a Student / copula cannot be rejected.(original abstract)
- Bekaert G., Harvey C. (1997): Emerging Equity Market Volatility. "Journal of Financial Economics", Vol. 43.
- Cech C. (2008): An Empirical Investigation of the Short-term Relationship between Interest Rate Risk and Credit Risk. [in:] Computational Finance and its Applications III. Eds. C. Brebbia, M. Costantino, M. Larran. WIT Press, Southampton 2008.
- Chen S., Poon S.H. (2007): Modelling International Stock Market Contagion Using Copula and Risk Appetite. Working Paper, Manchester Business School.
- Demarta S., McNeil A.J. (2005): The t Copula and Related Copulas. "International Statistical Review", Vol. 73, Iss. 1.
- Fama E.F. (1965): The Behavior of Stock Market Prices. "Journal of Business", Vol. 3, Iss. 1.
- Fortín I., Kuzmics C. (2002): Tail-dependence in Stock-Return Pairs. "International Journal of Intelligent Systems in Accounting, Finance and Management", Vol. 11.
- Genest C., Rivest L.P. (1993): Statistical Inference Procedures for Bivariate Archimedian Copulas. "Journal of the American Statistical Association", Vol. 88.
- Hurd M., Salmon M., Schleicher C. (2007): Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index. Bank of England Working, Paper No. 334.
- Junker M., Wagner N., Szimayer A. (2003): Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications, working paper.
- Kang L. (2008): Modeling the Dependence Structure between Bonds and Stocks: A Multivariate Copula Approach, working paper.
- Kole E., Koedijk K., Verbeek M. (2007): Selecting Copulas for Risk Management. "Journal of Banking and Finance", Vol. 31, Iss. 8.
- Kupiec P.H. (1995): Techniques for Verifying the Accuracy of Risk Management Models. "Journal of Derivatives", Vol. 3.
- Liang Z.H., Zhang W., Li S.S. (2007): Asymmetric Extreme Dependence in Chinese Futures Markets. [in:] Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing.
- Mandelbrot B. (1963): The Variation of Certain Speculative Prices. "Journal of Business", Vol. 36.
- Mashal R., Zeevi A. (2002): Beyond Correlation: Extreme Co-movements between Financial Assets, working paper.
- Miljković V., Radović O. (2006): Stylized Facts of Asset Returns: Case of BELEX. "Economics and Organization", Vol. 3, Iss. 2.
- Mina J., Xiao J.Y. (2001): Return to RiskMetrics: The Evolution of a Standard, RiskMetrics Group.
- Sklar A. (1959): Fonctions de Répartition à n dimension et leurs Marges. "Publications de l'Institut de Statistique de l'Université de Paris", Vol. 8.