Abstract
Dependence modelling and estimation is a key issue in the assessment of financial risk. It is common knowledge meanwhile that the multivariate normal model with linear correlation as its natural dependence measure is by no means an ideal model. We suggest a large class of models and a dependence function, which allows us to capture the complete extreme dependence structure of a portfolio. We also present a simple nonparametric estimation procedure of this function. To show our new method at work we apply it to a financial data set of high-frequency stock data and estimate the extreme dependence in the data. Among the results in the investigation we show that the extreme dependence is the same for different time scales. This is consistent with the result on high-frequency FX data reported in Hauksson et al. (2001). Hence, the different asset classes seem to share the same time scaling for extreme dependence. This time scaling property of high-frequency data is also explained from a theoretical point of view.
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Bingham, N.H., Goldie, C.M. & Teugels, J.L. (1987) Regular Variation. Cambridge University Press. Cambridge.
Breymann, W. Dias, A. & Embrechts, P. (2003). Dependence structures for multivariate highfrequency data in finance. Quantitative Finance 3: 1–14.
Brockwell, P.J. & Davis, R.A. (1991). Time Series: Theory and Methods, 2nd edition. Springer, New York.
Coles, S. G. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer, London.
Dias, A. & Embrechts, P. (2003). Dynamic copula models for multivariate high-frequency data in finance. Preprint, ETH Zurich.
Drost, F. C. & Nijman, T.E. (1993). Temporal aggregation of GARCH processes Econometrica 61: 909–927.
Embrechts, P. (Ed.) (2000). Extremes and Integrated Risk Management. UBS Warburg and Risk Books.
Embrechts, P., Klüppelberg, C. & Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.
Embrechts, P., Lindskog, F. & McNeil, A. (2001). Modelling dependence with copulas and applications to risk management. In: Rachev, S. (Ed.) Handbook of Heavy Tailed Distributions in Finance. Elsevier, Chapter 8, pp. 329–384.
Embrechts, P., McNeil, A. & Straumann, D. (2002). Correlation and dependence in risk managemant: properties and pitfalls. In: Dempster, M. and Moffatt, H.K. (Eds.) Risk Management: Value at Risk and Beyond. Cambridge University Press, Cambridge.
Hauksson, H., Dacorogna, M., Domenig, T., Müller, U. & Samorodnitsky, G. (2001) Multivariate extremes, aggregation and risk estimation. Quantitative Finance 1(1): 79–95.
Hsing, T., Klüppelberg, C. & Kuhn, G. (2004). Dependence estimation and visualization in multivariate extremes with applications to financial data. Extremes 7: 99–121.
Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall, London.
Klüppelberg, C. & Kuhn, G. (2009). Copula structure analysis. J. Royal Stat. Soc., Series B 71(3), 737–753.
Klüppelberg, C., Kuhn, G. & Peng, L. (2008). Semi-parametric models for the multivariate tail dependence function - the asymptotically dependent case. Scand. J. Stat. 35(4): 701–718.
Klüppelberg, C., Kuhn, G. & Peng, L. (2007). Estimating the tail dependence of an elliptical distribution. Bernoulli 13(1): 229–251.
Müller U. A., A. Dacorogna M. M. & Pictet, O. V. (1998). Heavy tails in high-frequency financial data. In: R.J. Adler, R. E. Feldman and M. S. Taqqu (Eds.) A Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy Tailed Distributions, Birkhäuser, Boston, MA, pp. 55–77.
Zhang, L. (2009). Estimating covariation: Epps effect, microstructure noise. Journal of Econometrics. To appear.
Acknowledgments
E.B. takes pleasure to thank Patrik Albin for generously providing the version the proof of Proposition 4, Holger Rootzén for fruitful discussions, Catalin Starica for suggesting the median filter and the Stochastic Center, Chalmers for a travelling grant. He also thanks the Center for Mathematical Sciences of the Munich University of Technology for a very stimulating and friendly atmosphere during a much needed research stay.
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Brodin, E., Klüppelberg, C. (2010). Modelling, Estimation and Visualization of Multivariate Dependence for High-frequency Data. In: Kneib, T., Tutz, G. (eds) Statistical Modelling and Regression Structures. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_15
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DOI: https://doi.org/10.1007/978-3-7908-2413-1_15
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