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Efficiently sampling exchangeable cuadras-auge copulas in high dimensions

INFORMATION SCIENCES 2009年第17期179卷 2872-2877页

作者： Mai, Jan-Frederik Scherer, Matthias Tech Univ Munich HVB Inst Math Finance D-85748 Garching Germany

An n-dimensional random vector is constructed whose survival copula is given by a copula that was first presented in cuadras and auge [C.M. cuadras, J. auge, A continuous general multivariate distribution and its properties, Communications in Statistics - Theory and Methods 10 (4) (1981) 339-353]. This construction adds a Poisson subordinator as mixing variable to initially independent exponentially distributed random variables. It is shown how the choice of Poisson process relates to the parameter of the induced cuadras-auge copula. Based on this construction, a sampling algorithm for this multivariate distribution is presented which has average computational efficiency O(n log log n). (C) 2008 Elsevier Inc. All rights reserved.

关键词： cuadras-auge copula Sampling algorithm Poisson process

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A comprehensive extension of the FGM copula

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STATISTICAL PAPERS 2017年第2期58卷 373-392页

作者： Hurlimann, Werner Feldstr 145 CH-8004 Zurich Switzerland

We consider one-parametric families of copulas for which the complement function for independence satisfies an anti-symmetric property. The Spearman rank correlation and Kendall's tau of an anti-symmetric family of copulas are necessarily odd functions of the parameter. Extending the parameter range of the FGM copula to the whole real line and truncated it from above and below using the Hoeffding-Fr,chet bounds generates a comprehensive anti-symmetric extension of the FGM copula. The detailed analytical representation of the extended FGM copula, the absolutely continuous and singular components, as well as the Spearman rank correlation and Kendall's tau dependence functions are derived. Several additional examples illustrate the anti-symmetric copula construction.

关键词： Hoeffding-Frechet bounds Anti-symmetry Spearman rho Kendall tau FGM copula cuadras-auge copula Chogosov copula

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Reparameterizing Marshall-Olkin copulas with applications to sampling

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2011年第1期81卷 59-78页

作者： Mai, Jan-Frederik Scherer, Matthias Tech Univ Munich HVB Inst Math Finance D-85748 Garching Germany

It is shown that exchangeable Marshall-Olkin survival copulas coincide with a parametric family of copulas studied in [J.-F. Mai and M. Scherer, Levy-Frailty copulas, J. Multivariate Anal. 100 (2009), pp. 1567-1585]. This observation implies an alternative probabilistic interpretation in many cases and allows the transfer of known results from one family to the other. For instance, using the classical construction of [A.W. Marshall and I. Olkin, A multivariate exponential distribution, J. Am. Stat. Assoc. 62 (1967), pp. 30-44], sampling an n-dimensional Marshall-Olkin copula requires 2n-1 exponentially distributed random variables, which is inefficient in large dimensions. Applying the alternative construction, sampling an exchangeable n-dimensional copula boils down to generating n independent exponentially distributed random variables and one path of a certain Levy subordinator, which is highly efficient in many cases. Furthermore, the alternative model and sampling methodology is generalized to high-dimensional hierarchical copulas. A sampling algorithm for the latter is described in detail and illustrated with an example.

关键词： Levy-frailty copula Marshall-Olkin copula cuadras-auge copula hierarchical copula n-monotone sequence

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A TRACTABLE MULTIVARIATE DEFAULT MODEL BASED ON A STOCHASTIC TIME-CHANGE

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INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE 2009年第2期12卷 227-249页

作者： Mai, Jan-Frederik Scherer, Matthias Tech Univ Munich HVB Inst Math Finance Boltzmannstr 3 D-85748 Garching Germany

A stochastic time-change is applied to introduce dependence to a portfolio of credit-risky assets whose default times are modeled as random variables with arbitrary distribution. The dependence structure of the vector of default times is completely separated from its marginal default probabilities, making the model analytically tractable. This separation is achieved by restricting the time-change to suitable Levy subordinators which preserve the marginal distributions. Jump times of the Levy subordinator are interpreted as times of excess default clustering. Relevant for practical implementations is that the parameters of the time-change allow for an intuitive economical explanation and can be calibrated independently of the marginal default probabilities. On a theoretical level, a so-called time normalization allows to compute the resulting copula of the default times. Moreover, the exact portfolio-loss distribution and an approximation for large portfolios under a homogeneous portfolio assumption are derived. Given these results, the pricing of complex portfolio derivatives is possible in closed-form. Three different implementations of the model are proposed, including a compound Poisson subordinator, a Gamma subordinator, and an Inverse Gaussian subordinator. Using two parameters to adjust the dependence structure in each case, the model is capable of capturing the full range of dependence patterns from independence to complete comonotonicity. A simultaneous calibration to portfolio-CDS spreads and CDO tranche spreads is carried out to demonstrate the model's applicability.

关键词： Levy subordinator cuadras-auge copula CDO pricing portfolio-loss process multivariate default model

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Discrete Bivariate Distributions Generated By copulas: DBEEW Distribution

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2019年第3期13卷 47-47页

作者： Najarzadegan, H. Alamatsaz, M. H. Kazemi, I. Univ Isfahan Dept Stat Esfahan Iran

copulas are the most powerful tools in constructing continuous multivariate distributions given marginals and certain dependence structures. In this paper, we shall propose a general and novel method of generating discrete bivariate distributions using copulas. The advantage of our method is that, contrary to the standard methods, we do not need to have the joint distribution of the base variables, but we only need the marginal distributions. In particular, we shall concentrate on generating a new family of discrete bivariate exponentiated extended Weibull (DBEEW) distribution by a cuadras-auge copula. We shall study several mathematical properties of a DBEEW distribution. Three special submodels of our new proposed distribution are studied in more detail. Finally, estimation of parameters for these three submodels is investigated and their potential and flexibility are examined using a real data set.

关键词： cuadras-auge copula Discrete bivariate distribution Estimation Probability generating function Renyi entropy

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