Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] M. Holtz. The computation of American option price sensitivities using a monotone multigrid method for higher order B-spline discretizations. 2004. Working paper.
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In this paper a fast solver for discrete free boundary value problems which is based on hierarchical higher order discretizations is presented. The numerical method consists of a finite element discretization with B-spline ansatz functions of arbitrary degree combined with a monotone multigrid method for the efficient solution of the resulting discrete system. In particular, the potential of the scheme in the fast and accurate computation of American style option prices in the Black-Scholes framework and of their derivatives with respect to the underlying is investigated. Due to the higher order discretization, the derivatives, also called Greek letters, can be stably and accurately determined via direct differentiation of the basis functions. Considering the valuation of plain vanilla American stock options, we show that our solution method is competitive to the best schemes proposed in the literature when accurate approximations to the derivatives are required. It provides the first multigrid approach based on higher order basis functions which is directly applicable to American option pricing.