We proposed a solution to the inhomogeneous Heston PDE via the geometric transformation proposed by Dell’Era (2010), and verify the solution by providing an analytical solution for the Heston PDE with a constant inhomogeneous term. Numerical benchmarks via ADI finite difference scheme are also provided. • Provide a solution of the Heston (stochastic volatility) PDE with an inhomogeneous term, via a sequence of transformations named ‘geometric transformation’ known in the literature. • Provide a closed-form solution of the case when the inhomogeneous term is a constant, as a proof of concept. • Provide numerical benchmark via ADI finite difference to verify the proposed solution.
Ce Wang (Sun,) studied this question.