Which Copula is the Right One?

Durrleman, Valdo; Nikeghbali, Ashkan; Roncalli, Thierry

doi:10.2139/ssrn.1032545

Cited by 118 publications

(64 citation statements)

References 15 publications

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“…These measures are based on a comparison between some empirical accurate approximations (that are usually computationally expensive) and the analyzed copula. 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] .…”

Section: Copula Approach Analysismentioning

confidence: 99%

“…Among the several families of available generic GOF tests in the literature, in [27] , Berg suggests that methods that rely on the so-called Deheuvels or empirical copula [31] give reliable results. Hence, we will perform a test which is based on the distances between the Deheuvels copula, C d , and the analyzed copula C (see [28] ). By using the discrete L 2 norm, this GOF measure reads…”

Section: Copula Approach Analysismentioning

confidence: 99%

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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%

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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show abstract

“…, u n ≤ u n(i) , where u (i) denotes the order statistic. A best copula within a class of the t copulas is chosen such that the distance of the empirical copulaĈ and the theoretical copula C is minimized (Durrleman et al, 2000). However, this does not mean that a copula chosen is a fitted model for data in an absolute sense.…”

Section: Copula Selection and Its Adequacymentioning

confidence: 99%

Analysis of Multiple Myeloma Life Expectancy Using Copula

Lee

Deng

Lee

2013

IJSP

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Multiple myeloma is a blood cancer that develops in the bone marrow. It is assumed that in most cases multiple myeloma develops in association with several medical factors acting together, although the leading cause of the disease has not yet been identified. In this paper, we investigate the relationship between the factors to measure multiple myeloma patients' survival time. For this, we employ a copula that provides a convenient way to construct statistical models for multivariate dependence. Through an approach via copulas, we find the most influential medical factors that affect the survival time. Some goodness-of-fit tests are also performed to check the adequacy of the copula chosen for the best combination of the survival time and the medical factors. Using the Monte Carlo simulation technique with the copula, we re-sample survival times from which the anticipated life span of a patient with the disease is calculated.

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“…Fisher (1997) pointed out two main reasons as to why copulas are of interest to statisticians: "Firstly, as a way of studying scale-free measures of dependence; and secondly, as a starting point for constructing families of bivariate distributions, sometimes with a view to simulation." Recently, numerous papers were published on the use of copulas for solving financial problems, such as those referred to Bouyé et al In Durrleman et al (2000), different types of copulas utilized in financial modelling are reviewed and compared. Joe (1996) Kauermann et al (2013) tackled non-and semi-parametric routines for copula estimation.…”

Section: Introductionmentioning

confidence: 99%

Polynomially Adjusted Saddlepoint Density Approximations

Provost

Sheng

2014

IJSP

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This thesis aims at obtaining improved bona fide density estimates and approximants by means of adjustments applied to the widely used saddlepoint approximation. Said adjustments are determined by solving systems of equations resulting from a moment-matching argument. A hybrid density approximant that relies on the accuracy of the saddlepoint approximation in the distributional tails is introduced as well. A certain representation of noncentral indefinite quadratic forms leads to an initial approximation whose parameters are evaluated by simultaneously solving four equations involving the cumulants of the target distribution. A saddlepoint approximation to the distribution of quadratic forms is also discussed. By way of application, accurate approximations to the distributions of the Durbin-Watson statistic and a certain portmanteau test statistic are determined. It is explained that the moments of the latter can be evaluated either by defining an expected value operator via the symbolic approach or by resorting to a recursive relationship between the joint moments and cumulants of sums of products of quadratic forms. As well, the bivariate case is addressed by applying a polynomial adjustment to the product of the saddlepoint approximations of the marginal densities of the standardized variables. Furthermore, extensions to the context of density estimation are formulated and applied to several univariate and bivariate data sets. In this instance, sample moments and empirical cumulant-generating functions are utilized in lieu of their theoretical analogues. Interestingly, the methodology herein advocated for approximating bivariate distributions not only yields density estimates whose functional forms readily lend themselves to algebraic manipulations, but also gives rise to copula density functions that prove significantly more flexible than the conventional functional type. ACKNOWLEDGEMENTSThere are many people I would like to thank for their support over the past three years.Firstly, I would like to express my gratitude to my supervisor, Dr. Serge Provost, for his valuable guidance, as well as his patience and keen enthusiasm to make this thesis possible.

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Which Copula is the Right One?

Abstract: In this paper, we give a few methods for the choice of copulas in financial modelling.

Cited by 118 publications

References 15 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

Analysis of Multiple Myeloma Life Expectancy Using Copula

Polynomially Adjusted Saddlepoint Density Approximations

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