Multiscale methods for the valuation of American options with stochastic volatility

This paper deals with the efficient valuation of American options. We adopt Heston’s approach for a model of stochastic volatility and derive a generalized Black Scholes equation. This leads to a parabolic boundary value problem with a free boundary, the optimal exercise price of the option. For its efficient numerical solution, we employ, among other multiscale methods, a monotone multigrid method based on linear finite elements in space and display corresponding numerical experiments.