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

  author = {T.~Gerstner and M.~Holtz},
  title = {Geometric Tools for the Valuation of Performance-Dependent
  booktitle = {Computational Finance and its Application II},
  year = {2006},
  editor = {M.~Costantino and C.A.~Brebbia},
  pages = {161--170},
  address = {London},
  publisher = {WIT Press.},
  annote = {series,ALM},
  abstract = {In this paper, we describe several methods for the
		  valuation of performance-dependent options. Thereby, we use
		  a multidimensional Black-Scholes model for the temporal
		  development of the asset prices. The martingale approach
		  then yields the fair price as a multidimensional integral
		  whose dimension is the number of stochastic processes in
		  the model. The integrand is typically discontinuous,
		  though, which makes accurate solutions difficult to achieve
		  by numerical approaches. However, using tools from
		  computational geometry we are able to derive a pricing
		  formula which only involves the evaluation of smooth
		  multivariate normal distributions. This way,
		  performance-dependent options can efficiently be priced
		  even for high-dimensional problems as it is shown by
		  numerical results.},
  pdf = { 1}