@TechReport{	  it:2006-028,
  author	= {Ulrika Pettersson and Elisabeth Larsson and Gunnar
		  Marcusson and Jonas Persson},
  title		= {Improved Radial Basis Function Methods for
		  Multi-Dimensional Option Pricing},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2006},
  number	= {2006-028},
  month		= may,
  abstract	= {In this paper, we have derived a radial basis function
		  (RBF) based method for the pricing of financial contracts
		  by solving the Black-Scholes partial differential equation.
		  As an example of a financial contract that can be priced
		  with this method we have chosen the multi-dimensional
		  European basket call option. We have shown numerically that
		  our scheme is second order accurate in time and spectrally
		  accurate in space for constant shape parameter. For other,
		  non-optimal choices of shape parameter values, the
		  resulting convergence rate is algebraic. We propose an
		  adaptive node point placement that improves the accuracy
		  compared with a uniform distribution. Compared with an
		  adaptive finite difference method, the RBF method is 20-40
		  times faster in one and two space dimensions and has
		  approximately the same memory requirements.}
}