@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.}
}