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.