[1] 
T. Gerstner and M. Holtz.
Valuation of performancedependent options.
Applied Mathematical Finance, 15(1):120, 2008. [ bib  .pdf 1 ] Performancedependent 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 performancedependent options. To this end, we use a multidimensional BlackScholes 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, performancedependent options can efficiently be priced even for highdimensional problems as it is shown by numerical results.
