Heston volatility model has received a growing attention amongst academics and practitioners for derivative pricing applications. Yet, the sensibility of the model parameters and instabilities of its analytic characteristic function for large derivatives and complex derivations make the model inconsistent and unreliable. As these parameters and function are defined and used in the complex plane, they potentially include ‘branching’. Therefore, additional parameter restrictions are required. This paper aims at providing insight on the sensitivity of the model parameterization and establishing an algorithm to ensure the stability of the analytic characteristic function under full dimensional and unrestricted parameter space.