Fitting bivariate cumulative returns with copulas

Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market

“…In Genest et al [12] various goodness of fit tests are proposed, but they are restricted to the arquimedean case. A recent paper similar in spirit to ours is that of Hürlimann [15], who presents some copula fitting results for bivariate daily cumulative returns between a market index and stocks. However, his analysis is restricted to the class of arquimedean copulas and different marginal distributions are considered.…”

“…Otherwise, the chi-square test would not hold. This assumption is also made in Mashal & Zeevi [23], Malavergne & Sornette [22] and implicitly in Hürlimann [15].…”

Asymptotic Value-at-Risk Estimates for Sums of Dependent Random Variables

“…Nevertheless it is quite difficult to fit copulas to real data (for successful real data fitting of copulas by actuaries see Klugman-Prasa [11] and Hürlimann [6]). It is difficult to have a good intuitive feeling for dependence structures (see e.g.…”

A Mean-Variance Portfolio Optimal Under Utility Pricing

“…The mixture of a normal with inverted gamma variance yields the Pearson type VII distribution or generalised Student t [4][5][6] . It has been proposed to model financial returns by Praetz [7] , Blattberg and Gonedes [8] , Kon [9] , Taylor [10] , Hürlimann [11,12] . An actuarial application is found in Hürlimann [13] .…”

“…Since a lot of bivariate random models satisfy the required linear regression property, the displayed covariance identity has a wide application. Among the many multivariate models satisfying linear regression properties, let us mention the following few but important classes and families of multivariate distributions: * The class of symmetric elliptical distributions [3] * Bivariate and multivariate distributions of Pearson type [36,37] * Bivariate and multivariate Pareto distributions of the first kind [38] * Bivariate and multivariate distributions constructed from linear Spearman or Fréchet copulas with margins from location-scale families [11,12,37,39] Appendix B: Numerical evaluation of two special integral functions First, we show how to compute the integral (2.30), that is where the integrals can be calculated recursively as follows (use partial integration) :…”