The project is devoted to the development and implementation of monotone multigrid methods, transparent boundary conditions and adaptive strategies for American option pricing. In cooperation with Deutsche Bank London various kinds of 1- and 2-factor models (local volatility, deterministic default, short rate models, Vasicek model, stock-stock model, Stock-Vasicek interest rate model, Stock-Hazard model, ....) will be considered. The project is driven by the mutual benefits of scientific research and direct applications in banking practice.