Abstract
The deterministic numerical valuation of American options under Heston's stochastic volatility model is considered. The prices are given by a linear complementarity problem with a two-dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values, while for large asset values and variance a standard truncation is used. The finite difference discretization is constructed by numerically solving a quadratic optimization problem aiming to minimize the truncation error at each grid point. A Lagrange approach is used to treat the linear complementarity problems. Numerical examples demonstrate the accuracy and effectiveness of the proposed approach.
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