Fixed point iterative methods for linear complementarity problems in American option pricing

Abstract

The linear complementarity formulation for American option pricing is studied. In particular, fixed point solution methods from literature are considered. Here simplified proofs for convergence criterion are provided. Further generalizations and modifications are also suggested alongside more tractable convergence analysis. Alternative formulations for the option pricing problem are also surveyed. These will be in the form of the Chapman-Kolmogorov lattice methods and the Modified Mellin transform framework. Some numerical experiments are then conducted for comparison purposes.