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In this study, we investigated one of the most popular stochastic volatility pricing models, the Heston model, for European options. This paper deals with the implementation of a finite difference scheme to solve a two-dimensional partial differential equation form of the Heston model. We explain in detail the explicit scheme for the Heston model, especially on the boundaries. Some simple ideas to modify the treatment on the boundaries, which leads to a lower computational cost, are also stated. The paper also covers comparisons between the explicit solution and the semi-analytical solution.

A Simulation of the Heston Model with Stochastic Volatility Using the Finite Difference Method