Mathematical and Statistical Methods for Actuarial Sciences and Finance

184 F. Lisi and E. Otranto a classification scheme that combines different statistical methodologies (principal component analys ...

Clustering mutual funds by return and risk levels 185 series. We suppose that the return dynamics can be described by the follow ...

186 F. Lisi and E. Otranto from which it is easy to derive the expected value at timetgiven past information Et− 1 (ε^2 t)= γ 1 ...

Clustering mutual funds by return and risk levels 187 3 An application As an application of the previously described procedure, ...

188 F. Lisi and E. Otranto 4 stars for(m,l),(h,m)(medium gain and low risk, high gain and medium risk); 5 stars for(h,l)(high ga ...

Clustering mutual funds by return and risk levels 189 Ta b le 2 .Comparison of Morningstar and Clustering Classification Differe ...

190 F. Lisi and E. Otranto definition of risk is linked to the estimation of a particular Threshold GARCH model, which character ...

Clustering mutual funds by return and risk levels 191 Otranto, E.: Clustering heteroskedastic time series by model-based proced ...

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Multivariate Variance Gamma and Gaussian dependence: a study with copulas∗ Elisa Luciano and Patrizia Semeraro Abstract.This pap ...

194 E. Luciano and P. Semeraro In the financial literature, different univariate Levy processes – able to capture ́ non-normalit ...

Multivariate Variance Gamma and Gaussian dependence: a study with copulas 195 2VGmodels The VGunivariatemodel for financial retu ...

196 E. Luciano and P. Semeraro It depends on three marginal parameters(μj,σj,αj)and an additional common parametera. Its charact ...

Multivariate Variance Gamma and Gaussian dependence: a study with copulas 197 Since the marginal and joint distributions in (5) ...

198 E. Luciano and P. Semeraro find the numerical copulaCˆtof the process over the prespecified grid; compute the distance betw ...

Multivariate Variance Gamma and Gaussian dependence: a study with copulas 199 Ta b le 1 .Calibrated parameters for theα-VG price ...

200 E. Luciano and P. Semeraro Ta b le 3 .Distances between the Gaussian and empirical copula for calibratedα-VG price processes ...

Multivariate Variance Gamma and Gaussian dependence: a study with copulas 201 Fig. 1.Level curves of the Gaussian (Gaus) and emp ...

202 E. Luciano and P. Semeraro approximate the actual copula with the Gaussian one, at least over long horizons, life becomes mu ...

Multivariate Variance Gamma and Gaussian dependence: a study with copulas 203 ObtainNrealisations(xn 1 ,x 2 n)ofX( 1 )by means ...