@InProceedings{	  Gerstner.Holtz.Korn:2006,
  author	= {T.~Gerstner and M.~Holtz and R.~Korn},
  title		= {Valuation of Performance-Dependent Options in a
		  {B}lack-{S}choles Framework},
  booktitle	= {Numerical Methods for Finance},
  pages		= {203--214},
  publisher	= {Chapman \& Hall/CRC},
  editor	= {J. Appleby and D. Edelman and J. Miller},
  year		= {2007},
  annote	= {proceedings,ALM},
  pdf		= {http://wissrech.ins.uni-bonn.de/research/pub/gerstner/holtz_gerstner_korn.pdf}
		  ,
  abstract	= {In this paper, we introduce performance-dependent options
		  as the appropriate financial instrument for a company to
		  hedge the risk arising from the obligation to purchase
		  shares as part of a bonus scheme for their executives. In
		  order to determine a fair price of such options, 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. As a remedy, we derive a pricing
		  formula which only involves the evaluation of smooth
		  multivariate normal distributions. This way,
		  performance-dependent options can efficiently be priced as
		  it is shown by numerical results.}
}