Pricing contemporary financial derivatives often require solving multidimensional partial differential equations with mixed derivatives. This paper presents an efficient hybrid approach to directly prescribes the dynamics of American option problems under the Heston stochastic volatility model. The algorithm developed involves trading the roles of financial variables which permit the problem to be solved inversely. The convergence of the algorithm is studied using a variational inequality approach, and we examine the solutions accuracy by comparison with those from existing methods. Furthermore, we explore the effects of time-dependent volatility on the optimal exercise prices.
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