Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {Markus Holtz},
  title = {The Computation of {American} Option Price Sensitivities
		  using a Monotone Multigrid Method for Higher Order
		  {B}-Spline Discretizations},
  note = {Working paper.},
  year = {2004},
  pdf = { 1},
  abstract = { 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. },
  annote = {article,ALM}