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

  author = {T.~Gerstner and M.~Holtz},
  title = {Valuation of Performance-Dependent Options},
  journal = {Applied Mathematical Finance},
  year = {2008},
  volume = {15},
  number = {1},
  pages = {1--20},
  annote = {article,ALM},
  abstract = {Performance-dependent options are financial derivatives
		  whose payoff depends on the performance of one asset in
		  comparison to a set of benchmark assets. In this paper, we
		  present a novel approach for the valuation of general
		  performance-dependent options. To this end, we use a
		  multidimensional Black-Scholes model to describe the
		  temporal development of the asset prices. The martingale
		  approach then yields the fair price of such options as a
		  multidimensional integral whose dimension is the number of
		  stochastic processes used in the model. The integrand is
		  typically discontinuous which makes accurate solutions
		  difficult to achieve by numerical approaches, though. Using
		  tools from computational geometry, we are able to derive a
		  pricing formula which only involves the evaluation of
		  several 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}