Tail dependence of the Gaussian copula revisited

Furman, Edward; Kuznetsov, Alexey; Su, Jianxi; Zitikis, Ričardas

doi:10.1016/j.insmatheco.2016.04.009

Cited by 13 publications

(8 citation statements)

References 26 publications

(33 reference statements)

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“…A discussion of the properties and disadvantages of these indices in the classification of extreme events is presented in refs. .…”

Section: Choice Of the Mixture In The Classification Process And Its mentioning

confidence: 99%

“…A discussion of the properties and disadvantages of these indices in the classification of extreme events is presented in refs. [7,8]. Plots of a mixture copula of Gumbel ( 1 = 1.5) and Clayton( 2 = 1) with = 0.5 on the left side and = 0.2 on the right side from those of multivariate normal models.…”

Section: Choice Of the Mixture In The Classification Process And Its mentioning

confidence: 99%

“…The indices of tail dependence typically used in the literature are defined in terms of copula behavior along the main diagonal path of C(u, u). However, the tail dependence of copulas can be substantially stronger along other paths [7,8]. For this reason, the authors were unable to capture the right degree of tail dependence.…”

Section: Figure 12mentioning

confidence: 99%

“…Refs. [7,8] present the decisive role of the diagonal path in measuring tail dependence copulas and propose a method to disregard the diagonal section of copulas when measuring tail dependence. This problem is not crucial to a ranking data framework.…”

Section: Figure 12mentioning

confidence: 99%

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Dissimilarity measure for ranking data via mixture of copulae*

Bonanomi

Ruscone

Osmetti

2019

Statistical Analysis

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We define a new distance measure for ranking data using a mixture of copula functions. Our distance measure evaluates the dissimilarity of subjects' ranking preferences to segment them via hierarchical cluster analysis. The proposed distance measure builds upon Spearman grade correlation coefficient on a copula transformation of rank denoting the level of importance assigned by subjects on the classification of k objects. These mixtures of copulae enable flexible modeling of the different types of dependence structures found in data and the consideration of various circumstances in the classification process. For example, by using mixtures of copulae with lower and upper tail dependence, we can emphasize the agreement on extreme ranks when they are considered important.

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“…A discussion of the properties and disadvantages of these indices in the classification of extreme events is presented in refs. .…”

Section: Choice Of the Mixture In The Classification Process And Its mentioning

confidence: 99%

Section: Choice Of the Mixture In The Classification Process And Its mentioning

confidence: 99%

Section: Figure 12mentioning

confidence: 99%

Section: Figure 12mentioning

confidence: 99%

See 2 more Smart Citations

Dissimilarity measure for ranking data via mixture of copulae*

Bonanomi

Ruscone

Osmetti

2019

Statistical Analysis

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“…Li [23]). Furman et al [17] study generalized notions of tail dependence. The tail order of Ledford and Tawn [21] (see also Hua and Joe [19]) provides a more refined measure of dependence in the tail.…”

Section: Introductionmentioning

confidence: 99%

Lower Tail Independence of Hitting Times of Two-Dimensional Diffusions

Saunders

Tsui

Iyengar

2017

Prob. Eng. Inf. Sci.

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The coefficient of tail dependence is a quantity that measures how extreme events in one component of a bivariate distribution depend on extreme events in the other component. It is well known that the Gaussian copula has zero tail dependence, a shortcoming for its application in credit risk modeling and quantitative risk management in general. We show that this property is shared by the joint distributions of hitting times of bivariate (uniformly elliptic) diffusion processes.

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A new family of modified Gaussian copulas for market consistent valuation of government guarantees

et al. 2022

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This paper deals with a copula-based stochastic dependence problem in the context of financial risks. We discuss the financial framework for assessing the theoretical up-front value of government guarantees on bank liabilities. EU States widely use these contracts to improve the financial system’s stability and manage the banking sector in crisis situations; in Italy, they have also been used to address the consequences of the Covid-19 emergency. From a market viewpoint, we deal with a defaultable guarantee contract where the State-guarantor and the bank-borrower are both subject to default risk, and their risks are interconnected. We show that the classical Gaussian copula is not satisfactory for modeling the dependence among the considered risks. Indeed, using the benchmark market model for credit risk portfolio management, we highlight some contradictory results observed for the up-front values of the guarantee when the default intensity of the guarantor is smaller than that of the borrower. Then, we introduce a new family of modified Gaussian copulas that overcomes the limitations of the standard approach, allowing to determine realistic results in terms of the guarantees “mark-to-model” value when the benchmark market model does not work. Numerical simulations validate the theoretical proposal.

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Tail dependence of the Gaussian copula revisited

Abstract: Abstract. Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk analysis.

Cited by 13 publications

References 26 publications

Dissimilarity measure for ranking data via mixture of copulae*

Dissimilarity measure for ranking data via mixture of copulae*

Lower Tail Independence of Hitting Times of Two-Dimensional Diffusions

A new family of modified Gaussian copulas for market consistent valuation of government guarantees

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