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Title:

Copula structure analysis

Description:

We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but differe...

We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula-based approach and the classical approach. Our new method yielear models also. Copyright Journal compilation (c) 2009 Royal Statistical Society. Minimize

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article

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Title:

Semi-Parametric Models for the Multivariate Tail Dependence Function - the Asymptotically Dependent Case

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In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension, non-parametrically estimating a tail dependence fun...

In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension, non-parametrically estimating a tail dependence function is very inefficient and fitting a parametric model to tail dependence functions is not robust. In this paper, we propose a semi-parametric model for (asymptotically dependent) tail dependence functions via an elliptical copula. Under this model assumption, we propose a novel estimator for the tail dependence function, which proves favourable compared to the empirical tail dependence function estimator, both theoretically and empirically. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008. Minimize

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Title:

Copula Structure Analysis

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In this paper we extend the standard approach of correlation structure analysis for dimension reduction of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a correlation-like structure remains...

In this paper we extend the standard approach of correlation structure analysis for dimension reduction of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behavior of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula based approach and the classical approach. Our new method yields a considerable dimension reduction also in non-linear models. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Klueppelberg/copstruc090118.pdf

http://www-m4.ma.tum.de/Papers/Klueppelberg/copstruc090118.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Copula structure analysis ; correlation structure analysis ; covariance structure analysis ; dimension reduction ; elliptical copula ; factor analysis ; Kendall’s tau

Copula structure analysis ; correlation structure analysis ; covariance structure analysis ; dimension reduction ; elliptical copula ; factor analysis ; Kendall’s tau Minimize

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Dependence estimation and visualization in multivariate extremes with application to financial data

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We investigate extreme dependence in a multivariate setting with special emphasis on financial applications. We introduce a new dependence function which allows us to capture the complete extreme dependence structure and present a nonparametric estimation procedure. The new dependence function is compared with existing measures including the spe...

We investigate extreme dependence in a multivariate setting with special emphasis on financial applications. We introduce a new dependence function which allows us to capture the complete extreme dependence structure and present a nonparametric estimation procedure. The new dependence function is compared with existing measures including the spectral measure and other devices measuring extreme dependence. We also apply our method to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-16

Source:

http://www-m4.ma.tum.de/pers/gabriel/DependenceEstimation.pdf

http://www-m4.ma.tum.de/pers/gabriel/DependenceEstimation.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Extreme dependence function ; nonparametric estimation ; financial data analysis

Extreme dependence function ; nonparametric estimation ; financial data analysis Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

On Dependence and Extremes

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This thesis deals with various topics on multivariate dependence structures and extremes. The first chapter investigates nonparametric estimation of multivariate extremes, where a new dependence function is developed, which allows for an easy understanding of multivariate extreme dependence. An additional focus there is the visualization of mult...

This thesis deals with various topics on multivariate dependence structures and extremes. The first chapter investigates nonparametric estimation of multivariate extremes, where a new dependence function is developed, which allows for an easy understanding of multivariate extreme dependence. An additional focus there is the visualization of multivariate extremes and a new concept is introduced. In contrast to many articles dealing with ’multivariate extreme dependence ’ only in the bivariate situation, we extend the estimation procedure and dependence function to arbitrary high dimensions. A problem arising when nonparametrically estimating multivariate extremes in higher dimensions is instability, hence there is an interest in flexible and finitely parameterized Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-17

Source:

http://www-m4.ma.tum.de/pers/gabriel/kuhn_gabriel-thesis.pdf

Document Type:

text

Language:

en

Subjects:

Nicht wissen ; was Wissen ist ; ist Leiden

Nicht wissen ; was Wissen ist ; ist Leiden Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Copula structure analysis based on robust and extreme dependence measures

Description:

In this paper we extend the standard approach of correlation structure analysis in order to reduce the dimension of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a ’correlation-like ’ struc...

In this paper we extend the standard approach of correlation structure analysis in order to reduce the dimension of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a ’correlation-like ’ structure remains but different margins and non-existence of moments are possible. Moreover, elliptical copulae allow also for a ’copula structure analysis ’ of dependence in extremes. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behavior of the statistics can be observed even for a sample of only 100 observations. Finally, we test our method on real financial data and explain differences between our copula based approach and the classical approach. Our new method yields a considerable dimension reduction also in non-linear models. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-16

Source:

http://www-m4.ma.tum.de/pers/gabriel/copstruc.pdf

http://www-m4.ma.tum.de/pers/gabriel/copstruc.pdf Minimize

Document Type:

text

Language:

en

Subjects:

copula structure analysis ; correlation structure analysis ; covariance structure analysis ; dimension reduction ; elliptical copula ; factor analysis ; Kendall’s tau ; tail copula

copula structure analysis ; correlation structure analysis ; covariance structure analysis ; dimension reduction ; elliptical copula ; factor analysis ; Kendall’s tau ; tail copula Minimize

DDC:

310 Collections of general statistics *(computed)*

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Title:

Tails of credit default portfolios

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We derive analytic expressions for the tail behavior of credit losses in a large homogeneous credit default portfolio. Our model is an extended Credit-Metrics model; i.e. it is a one-factor model with a multiplicative shock-variable. We show that the first order tail behavior is robust with respect to this shock-variable. In a simulation study w...

We derive analytic expressions for the tail behavior of credit losses in a large homogeneous credit default portfolio. Our model is an extended Credit-Metrics model; i.e. it is a one-factor model with a multiplicative shock-variable. We show that the first order tail behavior is robust with respect to this shock-variable. In a simulation study we compare different models for the latent variables. We fix default probability and correlation of the latent variables and the first order tail behavior of the limiting credit losses in all models and observe a completely different tail behavior leading to very different VaR esti-mates. For three portfolios of different credit quality we suggest a pragmatic model selection procedure and compare the fit with that of the β-model. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-07

Source:

http://www-m4.ma.tum.de/pers/gabriel/TailsOfCreditDefaults.pdf

http://www-m4.ma.tum.de/pers/gabriel/TailsOfCreditDefaults.pdf Minimize

Document Type:

text

Language:

en

Subjects:

β-model ; credit default portfolio ; extreme value theory ; heavy-tailed risk factor ; latent variable model ; multivariate t-distribution ; one factor model ; regular variation ; tail behavior of portfolio credit loss ; Value at Risk (VaR

β-model ; credit default portfolio ; extreme value theory ; heavy-tailed risk factor ; latent variable model ; multivariate t-distribution ; one factor model ; regular variation ; tail behavior of portfolio credit loss ; Value at Risk (VaR Minimize

DDC:

332 Financial economics *(computed)*

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Title:

Modelling, Estimation and Visualization of Multivariate Dependence for Risk Management

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Author for correspondence. Dependence modelling and estimation is a key issue in the assessment of portfolio risk. When measuring extreme risk in terms of the Value-at-Risk, the multivariate normal model with linear correlation as its natural dependence measure is by no means an ideal model. We suggest a large class of models and a new dependenc...

Author for correspondence. Dependence modelling and estimation is a key issue in the assessment of portfolio risk. When measuring extreme risk in terms of the Value-at-Risk, the multivariate normal model with linear correlation as its natural dependence measure is by no means an ideal model. We suggest a large class of models and a new dependence function which allows us to capture the complete extreme dependence structure of a portfolio. We also present a simple nonparametric estimation procedure. To show our new method at work we apply it to a financial data set of zero coupon swap rates and estimate the extreme dependence in the data. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Klueppelberg/DependenceEstimationJFEC.pdf

http://www-m4.ma.tum.de/Papers/Klueppelberg/DependenceEstimationJFEC.pdf Minimize

Document Type:

text

Language:

en

Subjects:

JEL Classifications ; C15 ; C52. Keywords ; Risk management ; extreme risk assessment ; multivariate models ; dependence function. 1 Risk management for extreme risk

JEL Classifications ; C15 ; C52. Keywords ; Risk management ; extreme risk assessment ; multivariate models ; dependence function. 1 Risk management for extreme risk Minimize

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Title:

Semi-parametric models for the multivariate tail dependence function – the asymptotically dependent case

Author:

Description:

In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail dependence functions. Even for moderate dimension, nonparametrically estimating a tail dependence funct...

In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail dependence functions. Even for moderate dimension, nonparametrically estimating a tail dependence function is very inefficient and fitting a parametric model to tail dependence functions is not robust. In this paper we propose a semi-parametric model for (asymptotically dependent) tail dependence functions via an elliptical copula. Based on this model assumption, we propose a novel estimator for the tail dependence function, which proves favorable compared to the empirical tail dependence function estimator, both theoretically and empirically. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Klueppelberg/SJS-06-111-rev1.pdf

http://www-m4.ma.tum.de/Papers/Klueppelberg/SJS-06-111-rev1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Asymptotic normality ; Dependence modeling ; Elliptical copula ; Elliptical distribution ; Regular variation ; Semi-parametric model ; Tail dependence function

Asymptotic normality ; Dependence modeling ; Elliptical copula ; Elliptical distribution ; Regular variation ; Semi-parametric model ; Tail dependence function Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Dimension reduction based on extreme dependence

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Description:

We introduce a dimension reduction technique based on extreme observations. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a fairly general model for the copula. We assume an elliptical copula to describe the extreme dependence structure, which preserves a ’correlation-l...

We introduce a dimension reduction technique based on extreme observations. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a fairly general model for the copula. We assume an elliptical copula to describe the extreme dependence structure, which preserves a ’correlation-like’ structure in the extremes. Based on the tail dependence function we estimate the copula correlation matrix, which is then analysed through classical dimension reduction techniques. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimator. Finally, we test our method on real financial data and explain differences between our copula based approach and the classical approach. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-02-18

Source:

http://www-m4.ma.tum.de/Papers/Haug/excopstruc100514.pdf

http://www-m4.ma.tum.de/Papers/Haug/excopstruc100514.pdf Minimize

Document Type:

text

Language:

en

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