Dual moments, volatility, dependence and the copula

Walking though the zoo of stochastic volatility and dependence parameters we got some ordering ideas and so detect some new species. The elementary volatility parameters of first and second order in spirit of dual theory of choice under risk or rank dependent expected utility are average absolute deviation and Gini index. Analogous to classical covariance dual dependence parameters will be introduced and investigated in connection with the copula of a multivariate distribution. It is argued that the dual volatility and dependence parameters are better suited than the classical parameters for applications in finance and insurance. From the technical point of view it is fascinating for a Choquet integrator to look at copulas, since for both theories ordering and comonotonicity play important roles.