On Kendall's Process

Barbe, Philippe; Genest, Christian; Ghoudi, Kilani; Rémillard, Bruno

doi:10.1006/jmva.1996.0048

Cited by 148 publications

(162 citation statements)

References 19 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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“….g., [3] or [22]. Moreover, note that applying T d for obtaining the transformed data U i , i ∈ {1, .…”

Section: A Goodness-of-fit Test For Archimedean Copulasmentioning

confidence: 99%

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

Hering

Hofert

2015

Innovations in Quantitative Risk Management

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A goodness-of-fit transformation for Archimedean copulas is presented from which a test can be derived. In a large-scale simulation study it is shown that the test performs well according to the error probability of the first kind and the power under several alternatives, especially in high dimensions where this test is (still) easy to apply. The test is compared to commonly applied tests for Archimedean copulas. However, these are usually numerically demanding (according to precision and runtime), especially when the dimension is large. The transformation underlying the newly proposed test was originally used for sampling random variates from Archimedean copulas. Its correctness is proven under weaker assumptions. It may be interpreted as an analogon to Rosenblatt's transformation which is linked to the conditional distribution method for sampling random variates. Furthermore, the suggested goodness-of-fit test complements a commonly used goodness-of-fit test based on the Kendall distribution function in the sense that it utilizes all other components of the transformation except the Kendall distribution function. Finally, a graphical test based on the proposed transformation is presented.

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“…In the general case (d ≥ 2), under some mild conditions, K n (t) has been shown by [1] to converge to a zero mean Gaussian process with a certain covariance function. These authors have also established the following useful representation…”

Section: N Can Be Viewed As a Sample Of Observations From K(θ T)mentioning

confidence: 99%

“…Step 3) Substitute the estimated cdf,Kα t; t * k,m , from step 2, for K(θ, t) in the expression (5), due to [1] and solve the ordinary differential equation (5) in order to express the estimator of the generator,φθ(t), in terms ofKα t; t * k,m . Then, using the definition (2) obtain an estimate of the Archimedean copulaĈθ(u 1 , .…”

Section: The Ged Spline Archimedean Copula Estimation Proceduresmentioning

confidence: 99%

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GeD spline estimation of multivariate Archimedean copulas

Dimitrova¹,

Kaishev²,

Penev

2008

Computational Statistics & Data Analysis

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A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so called Geometrically Designed splines (GeD splines), recently introduced by Kaishev et al. (2006 a,b) [10] and [11], to represent the cdf of a random variable W θ , obtained through the probability integral transform of an Archimedean copula with parameter θ. Sufficient conditions for the GeD spline estimator to posses the properties of the underlying theoretical cdf, K(θ, t), of W θ , are given. The latter conditions allow for defining a three-step estimation procedure for solving the resulting non-linear regression problem with linear inequality constraints. In the proposed procedure, finding the number and location of the knots and the coefficients of the unconstrained GeD spline estimator and solving the constraint least-squares optimisation problem, are separated. Thus, the resulting spline estimatorK(θ, t) is used to recover the generator and the related Archimedean copula by solving an ordinary differential equation. The proposed method is truly multivariate, it brings about numerical efficiency and as a result can be applied with large volumes of data and for dimensions d ≥ 2, as illustrated by the numerical examples presented.

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On Kendall's Process

Cited by 148 publications

References 19 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

Goodness-of-fit Tests for Archimedean Copulas in High Dimensions

GeD spline estimation of multivariate Archimedean copulas

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