Fitting bivariate loss distributions with copulas

Klugman, Stuart A.; Parsa, Rahul

doi:10.1016/s0167-6687(98)00039-0

Cited by 171 publications

(107 citation statements)

References 7 publications

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“…As a result, the existing critical values for the classical Anderson-Darling and the χ 2 tests are no longer valid. This problem is also noted by Klugman and Parsa (1999) and Malevergne and Sornette (2003). In their test for the normal copula for multivariate i.i.d.…”

Section: Introductionmentioning

confidence: 96%

Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates

Chen¹,

Fan

Patton

2004

SSRN Journal

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Evidence that asset returns are more highly correlated during volatile markets and during market downturns (see Longin andSolnik, 2001, andAng and has lead some researchers to propose alternative models of dependence. In this paper we develop two simple goodness-of-fit tests for such models. We use these tests to determine whether the multivariate Normal or the Student's t copula models are compatible with U.S. equity return and exchange rate data. Both tests are robust to specifications of marginal distributions, and are based on the multivariate probability integral transform and kernel density estimation. The first test is consistent but requires the estimation of a multivariate density function and is recommended for testing the dependence structure between a small number of assets. The second test may not be consistent against all alternatives but it requires kernel estimation of only a univariate density function, and hence is useful for testing the dependence structure between a large number of assets. We justify our tests for both observable multivariate strictly stationary time series and for standardized innovations of GARCH models. A simulation study demonstrates the efficacy of both tests. When applied to equity return data and exchange rate return data, we find strong evidence against the normal copula, but little evidence against the more flexible Student's t copula.

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Section: Introductionmentioning

confidence: 96%

Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates

Chen¹,

Fan

Patton

2004

SSRN Journal

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“…This work was partially supported by the James S. Mc Donnell Foundation 21st century scientist award/studying complex system. Some progress may be expected from the concept of copulas, recently proposed to be useful for financial applications , Frees and Valdez (1998), Haas (1999), Klugman and Parsa (1999)]. This concept has the desirable property of decoupling the study of the marginal distribution of each asset from the study of their collective behavior or dependence.…”

Section: Introductionmentioning

confidence: 99%

Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

Malevergne

Sornette

2001

SSRN Journal

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Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student's copula, cannot be rejected if it has sufficiently many "degrees of freedom". As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the correlation coefficient between the pair of asset is too high as the tail dependence neglected by the Gaussian copula can be as large as 0.6, i.e., three out five extreme events which occur in unison are missed.JEL Classification: C12, C15, F31, G19

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“…Several other authors among others, have used (for e.g., Klugman and Parsa (1999) and Chen and Fan (2005)) this data set to demonstrate copula-model selection and fitting in an insurance context. We conjecture that this data might well be explained by one or more bivariate Kumaraswamy copula models derived in this paper.…”

Section: An Application To Insurance Datamentioning

confidence: 99%

Bivariate Kumaraswamy Models via Modified Symmetric FGM Copulas: Properties and Applications in Insurance Modeling

Ghosh¹

2017

Preprint

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A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of (Farlie-GumbelMorgenstern) FGM bivariate copula for constructing several different bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions by this method allows for greater flexibility in the values of Spearman's correlation coefficient, ρ and Kendall's τ . For illustrative purposes, one representative data set is utilized to exhibit the applicability of these proposed bivariate copula models.

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Fitting bivariate loss distributions with copulas

Cited by 171 publications

References 7 publications

Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates

Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates

Testing the Gaussian Copula Hypothesis for Financial Assets Dependences

Bivariate Kumaraswamy Models via Modified Symmetric FGM Copulas: Properties and Applications in Insurance Modeling

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