Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be co...

This paper studies the problem of default correlation. We first introduce a random variable called “timeuntil-default” to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the jo...

In this paper, we will describe Monte Carlo simulations of the multivariate distributions with different marginals. This approach demands the joint distribution to be known (marginals models can be fitted using different distributional specifications, including nonnormal distributions) and it uses copula theory as a fundamental tool in modeling multivariate distribution. The copula theory allow...

Hydrological multivariate analysis has been widely studied using copula-based modelling, in which marginal distribution inference is one of the key issues. The main object of this study is to discuss the applicability of the principle of maximum entropy (POME) in marginal distribution inference, thus to develop a POME-copula framework to analyse the dependence of hydrological variables. Margina...

In recent years special attention has been devoted to the problem of finding a copula, the diagonal section and opposite diagonal section of which are known. For given diagonal function and opposite diagonal functions, we provide necessary and sufficient conditions for the existence of a copula to have these functions as diagonal and opposite diagonal sections. We make use of techniques related...

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses ‘Probability-Proportional-to-Size’ random s...

This paper studies the problem of default correlation. We first introduce a random variable called “timeuntil-default” to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the jo...

This paper develops a testing framework for comparing the predictive accuracy of competing multivariate density forecasts with different predictive copulas, focusing on specific parts of the copula support. The tests are framed in the context of the Kullback– Leibler Information Criterion, using (out-of-sample) conditional likelihood and censored likelihood in order to focus the evaluation on t...

We propose a copula based statistical method of fitting joint cumulative returns between a market index and a stock from the index family to daily data. Modifying the method of inference functions for margins (IFM method), we perform two separate maximum likelihood estimations of the univariate marginal distributions, assumed to be normal inverse gamma mixtures with kurtosis parameter equal to ...

To examine the asymmetry of financial data in detail, we have considered both the tail dependence with diverse copulas and Jung et al.’s [8] directional dependence by copula. From the empirical study in this paper, we have found that the tail dependence by Patton’s [11] modified symmetrized Joe-Clayton copula function did not show the asymmetry property sufficiently because there is no tail dep...