Copulas from the Fokker-Planck equation

We develop a theoretical framework addressing the joint distribution and provide a general equation for time-dependent copulas related to stochastic processes that arise in finance. The copula is a function that links univariate distributions to a joint multivariate distribution. The tractability and importance of a copula lie in the inference function for margins (IFM) method which is very suitable to use to achieve an understanding of many correlated statistical objects. We derive a parabolic equation for the copula governing the stochastic behavior with independent drifts and volatilities of multivariate objects. In fact, the Fokker-Planck equation for the stochastic differential equations with independent drifts and volatilities is modeled for the IFM. We also present numerical results which illustrate several sensitivity analyses of our scheme.