Dual volatility and dependence parameters and the copula

We introduce some new species into the zoo of stochastic volatility and dependence parameters. We start with average absolute deviation and Gini index, which are elementary volatility parameters of first and second order in spirit of dual theory of choice under risk or rank dependent expected utility. Similar to classical covariance we introduce dual dependence parameters and investigate them in connection with the copula of a bivariate 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.