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...

Modeling the joint tails of multiple financial time series has many important implications for risk management. Classical models dependence often encounter a lack fit in tails, calling additional flexibility. This paper introduces new semiparametric time-varying mixture copula model, which both weights and parameters are deterministic unspecified functions time. We propose penalized with group ...

The cumulative distribution network (CDN) [21] is a recently developed class of probabilistic graphical models (PGMs) permitting a copula factorization, in which the CDF, rather than the density, is factored. Despite there being much recent interest within the machine learning community about copula representations, there has been scarce research into the CDN, its amalgamation with copula theor...

The famous Sklar’s theorem (see [54]) allows to build multivariate distributions using a copula and marginal distributions. For the basic theory on copulas see the first chapter ([14]) or the books on copulas by Joe ([32]) and Nelson ([51]). Much emphasis has been put on the bivariate case and in [32] and [51] many examples of bivariate copula families are given. However the class of multivaria...

This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best-fit copula. Thereafter, simulation of copulas and bivariat...

In this paper, we address the crucial problems of parameters estimation of Collateralized Debt Obligation (CDO). We present a methodology for fair spread estimation of reconstituted (CDO) from European market data. A fundamental part of the pricing framework is the estimation of default probabilities and the structure of dependency. We present a copula based simulation procedure for pricing CDO...

We propose two new principal component analysis methods in this paper utilizing a semiparametric model. The according methods are named Copula Component Analysis (COCA) and Copula PCA. The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. The COCA and Copula PCA accordingly estimate the leading eigenvectors of ...