A New Howard–Crandall–Douglas Algorithm for the American Option Problem in Computational Finance
The unavailability of a closed-form formula for the American option price means that the price needs to be approximated by numerical techniques. The valuation problem can be formulated either as a linear complementarity problem or a free-boundary value problem. Both approaches require a discretisation of the associated partial differential equation, and it is common to employ standard second-order finite difference approximations. This work develops a new procedure for the linear complementarity formulation. Howard’s algorithm is used to solve the discrete problem obtained through a higher-order Crandall–Douglas discretisation. Speed and error comparisons indicate that this approach is more efficient than the procedures for solving the free-boundary value problem.
KeywordsComputational finance American option Policy iteration Howard’s algorithm
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