@TechReport{ it:2004-055,
author = {Per L{\"o}tstedt and Jonas Persson and von Sydow, Lina and
Johan Tysk},
title = {Space-Time Adaptive Finite Difference Method for
{E}uropean Multi-Asset Options},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2004},
number = {2004-055},
month = dec,
abstract = {The multi-dimensional Black-Scholes equation is solved
numerically for a European call basket option using \emph{a
priori}--\emph{a posteriori} error estimates. The equation
is discretized by a finite difference method on a Cartesian
grid. The grid is adjusted dynamically in space and time to
satisfy a bound on the global error at the expiry date. The
discretization errors in each time step are estimated and
weighted by the solution of the adjoint problem. Bounds on
the local errors and the adjoint solution are obtained by
the maximum principle for parabolic equations. The
performance of the method is illustrated by examples in
one, two, three, and four dimensions.}
}