B–Spline Based Monotone Multigrid Methods, with an Application to the Prizing of American Options
نویسندگان
چکیده
We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expansion coefficients. To illustrate the potential of the scheme, the method is applied to the pricing of American options in the Black–Scholes framework.
منابع مشابه
B-Spline-Based Monotone Multigrid Methods
Abstract. For the efficient numerical solution of elliptic variational inequalities on closed convex sets, multigrid methods based on piecewise linear finite elements have been investigated over the past decades. Essential for their success is the appropriate approximation of the constraint set on coarser grids which is based on function values for piecewise linear finite elements. On the other...
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