1,461 research outputs found
Copulas with given values on a horizontal and a vertical section
summary:In this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented
Out-of-sample comparison of copula specifications in multivariate density forecasts
We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or non-nested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student's t copula is favored over Gaussian, Gumbel and Clayton copulas. This suggests that these exchange rate returns are characterized by symmetric tail dependence.
Out-of-sample comparison of copula specifications in multivariate density forecasts
We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or nonnested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student’s t copula is favored over Gaussian, Gumbel and Clayton copulas. This suggests that these exchange rate returns are characterized by symmetric tail dependence.Copula-based density forecast; semiparametric statistics; out-of-sample forecast evaluation; Kullback-Leibler Information Criterion; empirical copula
Perturbed Copula: Introducing the skew effect in the co-dependence
Gaussian copulas are widely used in the industry to correlate two random
variables when there is no prior knowledge about the co-dependence between
them. The perturbed Gaussian copula approach allows introducing the skew
information of both random variables into the co-dependence structure. The
analytical expression of this copula is derived through an asymptotic expansion
under the assumption of a common fast mean reverting stochastic volatility
factor. This paper applies this new perturbed copula to the valuation of
derivative products; in particular FX quanto options to a third currency. A
calibration procedure to fit the skew of both underlying securities is
presented. The action of the perturbed copula is interpreted compared to the
Gaussian copula. A real worked example is carried out comparing both copulas
and a local volatility model with constant correlation for varying maturities,
correlations and skew configurations.Comment: 34 pages, 6 figures and 3 table
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Methods of Tail Dependence Estimation
Characterization and quantification of climate extremes and their dependencies are fundamental to the studying of natural hazards. This chapter reviews various parametric and nonparametric tail dependence coefficient estimators. The tail dependence coefficient describes the dependence (degree of association) between concurrent extremes at different locations. Accurate and reliable knowledge of the spatial characteristics of extremes can help improve the existing methods of modeling the occurrence probabilities of extreme events. This chapter will review these methods and use two case studies to demonstrate the application of tail dependence analysis
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