Valuation of Performance‐Dependent Options

Abstract

Performance‐dependent options are financial derivatives whose payoff depends on the performance of one asset in comparison to a set of benchmark assets. This paper presents a novel approach to the valuation of general performance‐dependent options. To this end, a multidimensional Black–Scholes model is used 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...