Elliptical Copulae with Dynamic Conditional Correlation

dependence;DCC;elliptical copula

Liu, Feng ; Dr. David Dickey, Committee Member,Dr. John Monahan, Committee Member,Dr. Denis Pelletier, Committee Member,Dr. Peter Bloomfield, Committee Chair,Liu, Feng ; Dr. David Dickey ; Committee Member ; Dr. John Monahan ; Committee Member ; Dr. Denis Pelletier ; Committee Member ; Dr. Peter Bloomfield ; Committee Chair

University:North Carolina State University

关键词: dependence;    DCC;    elliptical copula;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4875/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

Knowledge of the joint distribution is crucial for risk measure estimation, portfolio allocation, derivative pricing, to name but a few problems. The multivariate normal function, the most commonly used joint distribution, is not sufficient if data have features of fat tailed margins and co-extreme movements, which are commonly found in financial data. More flexible multivariate distributions are needed in order to address these features. The copula, originated by Sklar (1959) and also calledthe dependence function, can be combined with arbitrary marginal distributions to form various joint distributions. "Conditional copulae", proposed by Patton (2002a), are adopted by several researchers to introduce time-varying dependence beyond the existing time-varying variance-covariance. All the research thus far is focused on bivariate series. How to extend the models to higher dimension is not obvious. In the financial world, it is essential to develop models for high dimensional data that do not suffer the "curse of dimension" problem, but are still rich enough to capture the major data features, such as fat-tailed margins, volatility clustering, time-varying correlation and tail dependence.Motivated by Chen et al. (2004), we propose a model of "Elliptical Copulae with Dynamic Conditional Correlation" as the dependence model for some financial data. With additional information about the margins, the joint distribution is obtained in a straightforward way. Combining the good properties of copulae and DCC models, our model is especially attractive for high dimensional data. The general ideas of our model are as follows: each individual series is modelled by its own appropriate heteroskedasticity model, and standardized residuals are obtained after filtering out the estimated dynamic variance; then the standardized residuals are monotonically transformed to new ones as from the same univariate elliptical distribution; finally, the transformed residuals are used to build the dependence model of elliptical copulae with time-varying correlation from the corresponding elliptical DCC models.Our model is applied to two financial practices: VaR estimation and optimal portfolio allocation. The impacts of fat-tailed margins, time-varying correlation and tail dependence are investigated with two hypothetical portfolios. For VaR estimation, these data features have substantial importance; while for portfolio allocation, the effects are not so significant.