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This paper first studies the theoretical properties of the tail quotient correlation coefficient (TQCC) which was proposed to measure tail dependence between two random variables. By introducing random thresholds in TQCC, an approximation theory between conditional tail probabilities is established. The new random threshold-driven TQCC can be used to test the null hypothesis of tail independence under which TQCC test statistics are shown to follow a Chi-squared distribution under two general scenarios. The TQCC is shown to be consistent under the alternative hypothesis of tail dependence with a general approximation of max-stable distribution. Second, we apply TQCC to investigate tail dependencies of a large scale problem of daily precipitation in the continental US. Our results, from the perspective of tail dependence, reveal nonstationarity, spatial clusters, and tail dependence from the precipitations across the continental US.

This paper first studies the theoretical properties of the tail quotient correlation coefficient (TQCC) which was proposed to measure tail dependence between two random variables. By introducing random thresholds in TQCC, an approximation theory between conditional tail probabilities is established. The new random threshold-driven TQCC can be used to test the null hypothesis of tail independence under which TQCC test statistics are shown to follow a Chi-squared distribution under two general scenarios. The TQCC is shown to be consistent under the alternative hypothesis of tail dependence with a general approximation of max-stable distribution. Second, we apply TQCC to investigate tail dependencies of a large scale problem of daily precipitation in the continental US. Our results, from the perspective of tail dependence, reveal nonstationarity, spatial clusters, and tail dependence from the precipitations across the continental US.

In this paper we apply MGB2 distribution to price synthetic CDO. MGB2 distribution has flexible dependence structure and it is suitable to model extreme risk. The monotonicity of the spread of equity tranche with respect to some parameter is shown. We compare our model with the onefactor Gaussian, Clayton and double t models. Although our proposed MGB2 model is not flexible enough to produce the implied compound correlation smile, it is much more flexible to produce the patterns of base correlation curve than the others. Besides, concerning base correlation, MGB2 and double t model match the market data better than the Gaussian and Clayton copula models.