621 research outputs found
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
The Copula Approach to Sample Selection Modelling: An Application to the Recreational Value of Forests
The sample selection model is based upon a bivariate or a multivariate structure, and distributional assumptions are in this context more severe than in univariate settings, due to the limited availability of tractable multivariate distributions. While the standard FIML estimation of the selectivity model assumes normality of the joint distribution, alternative approaches require less stringent distributional hypotheses. As shown by Smith (2003), copulas allow great flexibility also in FIML models. The copula model is very useful in situations where the applied researcher has a prior on the distributional form of the margins, since it allows separating their modelling from that of the dependence structure. In the present paper the copula approach to sample selection is first compared to the semiparametric approach and to the standard FIML, bivariate normal model, in an illustrative application on female work data. Then its performance is analysed more thoroughly in an application to Contingent Valuation data on recreational values of forests.Contingent valuation, Selectivity bias, Bivariate models, Copulas
Estimation and Model Selection of Semiparametric Multivariate Survival Functions under General Censorship
Many models of semiparametric multivariate survival functions are characterized by nonparametric marginal survival functions and parametric copula functions, where different copulas imply different dependence structures. This paper considers estimation and model selection for these semiparametric multivariate survival functions, allowing for misspecified parametric copulas and data subject to general censoring. We first establish convergence of the two-step estimator of the copula parameter to the pseudo-true value defined as the value of the parameter that minimizes the KLIC between the parametric copula induced multivariate density and the unknown true density. We then derive its root--n asymptotically normal distribution and provide a simple consistent asymptotic variance estimator by accounting for the impact of the nonparametric estimation of the marginal survival functions. These results are used to establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application of the model selection test to the Loss-ALAE insurance data set is provided.Multivariate survival models, Misspecified copulas, Penalized pseudo-likelihood ratio, Fixed or random censoring, Kaplan-Meier estimator
An overview of the goodness-of-fit test problem for copulas
We review the main "omnibus procedures" for goodness-of-fit testing for
copulas: tests based on the empirical copula process, on probability integral
transformations, on Kendall's dependence function, etc, and some corresponding
reductions of dimension techniques. The problems of finding asymptotic
distribution-free test statistics and the calculation of reliable p-values are
discussed. Some particular cases, like convenient tests for time-dependent
copulas, for Archimedean or extreme-value copulas, etc, are dealt with.
Finally, the practical performances of the proposed approaches are briefly
summarized
Robustness of a semiparametric estimator of a copula
Copulas offer a convenient way of modelling multivariate observations and capturing the intrinsic dependence between the components of a multivariate random variable. A semiparametric method for estimating the dependence parameters of copulas was proposed by Genest, Ghoudi and Rivest (1995), in which the marginal distributions are estimated nonparameterically by empirical distribution functions. Thus, this method does not require any marginal distribution to have a known parametric form. However, a standard concern about semiparametric methods is the possibility that it may be substantially less efficient than the parametric method when the model is completely parametric and correctly specified. In this paper we investigate the efficiency-robustness properties of the foregoing semiparametric method by simulation; in particular, we evaluate the performance of this method when the marginal distributions are specified correctly and when they are specified incorrectly. The results show that the semiparametric method is better than the parametric methods. An example involving the household expenditure data for Australia is used to compare and contrast the methodsCopulas; multivariate joint distribution; inference function method;maximum likelihood mathod;semiparametric method
A test for Archimedeanity in bivariate copula models
We propose a new test for the hypothesis that a bivariate copula is an
Archimedean copula. The test statistic is based on a combination of two
measures resulting from the characterization of Archimedean copulas by the
property of associativity and by a strict upper bound on the diagonal by the
Fr\'echet-upper bound. We prove weak convergence of this statistic and show
that the critical values of the corresponding test can be determined by the
multiplier bootstrap method. The test is shown to be consistent against all
departures from Archimedeanity if the copula satisfies weak smoothness
assumptions. A simulation study is presented which illustrates the finite
sample properties of the new test.Comment: 18 pages, 2 figure
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