The Risk of Individual Stocks’ Tail Dependence with the Market and Its Effect on Stock Returns

Figure 1

Four detailed pictures of Copula density functions. To visualize their joint probability distributions and dependence structures between variables, this figure shows the surface of the densities for Gaussian and Student’s Copulas with various parameter values. The formulas of two Copula densities can be referred to Cherubini et al. [17]. Gaussian Copula only has one parameter, the correlation coefficient . While Student’s Copula has two parameters, the correlation coefficient and the degree of freedom , the latter controls the level dependence in tails. And when approaches infinity, the Student’s Copula would degenerate to Gaussian Copula.

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