@Article{ Gerstner.Holtz:2006*1,
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 = {http://wissrech.ins.uni-bonn.de/research/pub/gerstner/p_options.pdf}
}