Statistical Inference Procedures for Bivariate Archimedean Copulas

Genest, Christian; Rivest, Louis‐Paul

doi:10.1080/01621459.1993.10476372

Cited by 859 publications

(192 citation statements)

References 25 publications

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“…According to the work of Durrleman et al in [28] , we split the analysis, first evaluating the Archimedean copulas and subsequently, after choosing the optimal copula from this class, performing an analysis of the remaining copulas. The GOF testing for Archimedean copulas is a graphic procedure based on Kendall's processes, proposed by Genest and Rivest [29] and Barbe et al [30] . They defined a function K by…”

Section: Copula Approach Analysismentioning

confidence: 99%

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Leitao

Grzelak

Oosterlee

2017

Applied Mathematics and Computation

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a b s t r a c tIn this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan's analytic formula for short maturities that may be employed for model calibration purposes.

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Section: Copula Approach Analysismentioning

confidence: 99%

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Leitao

Grzelak

Oosterlee

2017

Applied Mathematics and Computation

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“…Because of the better performance in the test of Genest and Rivest (1993), we finally chose the Joe-copula for the statistical model of coinciding flood events. The superposi- tion of a copula-generated trivariate sample and the observed flood peaks in the first row of Fig.…”

Section: Selection Of Copulasmentioning

confidence: 99%

Extensive spatio-temporal assessment of flood events by application of pair-copulas

Schulte

Schumann

2015

Proc. IAHS

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Abstract. Although the consequences of floods are strongly related to their peak discharges, a statistical classification of flood events that only depends on these peaks may not be sufficient for flood risk assessments. In many cases, the flood risk depends on a number of event characteristics. In case of an extreme flood, the whole river basin may be affected instead of a single watershed, and there will be superposition of peak discharges from adjoining catchments. These peaks differ in size and timing according to the spatial distribution of precipitation and watershed-specific processes of flood formation. Thus, the spatial characteristics of flood events should be considered as stochastic processes. Hence, there is a need for a multivariate statistical approach that represents the spatial interdependencies between floods from different watersheds and their coincidences. This paper addresses the question how these spatial interdependencies can be quantified. Each flood event is not only assessed with regard to its local conditions but also according to its spatio-temporal pattern within the river basin. In this paper we characterise the coincidence of floods by trivariate Joe-copula and pair-copulas. Their ability to link the marginal distributions of the variates while maintaining their dependence structure characterizes them as an adequate method. The results indicate that the trivariate copula model is able to represent the multivariate probabilities of the occurrence of simultaneous flood peaks well. It is suggested that the approach of this paper is very useful for the risk-based design of retention basins as it accounts for the complex spatio-temporal interactions of floods.

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“…Genest & Rivest (1993) provided a graphical method allowing the comparison of different parametric distributions K with the empirical counterpart. In Vandenhende & Lambert (2000), copula selection was done using Akaike's information criteria from the ML fit of several copula models having the same marginal components.…”

Section: Frankmentioning

confidence: 99%

“…As discussed by Genest & Rivest (1993), a graphical comparison of the plot of K(p) − p versus p to its empirical counterpart is informative to assess whether the dependence has an Archimedean structure. In the Archimedean class, K(p) − p is always positive and has a first order derivative greater than or equal to −1 on all [0, 1].…”

Section: Least-squares Estimationmentioning

confidence: 99%

Local dependence estimation using semiparametric archimedean copulas

Vandenhende

Lambert

2005

Can. J. Statistics

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Abstract:The authors define a new semiparametric Archimedean copula family having a flexible dependence structure. The family's generator is a local interpolation of existing generators. It has locally-defined dependence parameters. The authors present a penalized constrained least-squares method to estimate and smooth these parameters. They illustrate the flexibility of their dependence model in a bivariate survival example.Estimation de la dépendance locale sur base de copules archimédiennes semiparamétriques Résumé : Les auteurs définissent une nouvelle famille de copules archimédiennes semiparamétriques dont la structure de dépendance est flexible. Le générateur de la famille est une interpolation locale de généra-teurs existants. Ses paramètres de dépendance sont définis localement. Les auteurs présentent une méthode de moindres carrés contraints pénalisés permettant l'estimation lisse de ces paramètres. Ils illustrent la flexibilité de leur modèle de dépendance dans un exemple de survie bivariée.

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Statistical Inference Procedures for Bivariate Archimedean Copulas

Cited by 859 publications

References 25 publications

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Extensive spatio-temporal assessment of flood events by application of pair-copulas

Local dependence estimation using semiparametric archimedean copulas

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