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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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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