Copulas for Stochastic Volatility Models

In this article, a Fokker–Planck equation framework for the copula density associated with a two-dimensional stochastic differential equations system is developed. The different information pieces associated with the statistical interdependence properties and the marginal ones are separated explicitly, and the corresponding boundary conditions for the copula distribution are analyzed. Given the set of functions that defines the copula density dynamics and the marginal probability density functions, a Fokker-Planck equation for the multivariate density probability function of the stochastic volatility model is obtained.