Valuation of performance-dependent options in a Black- Scholes framework
نویسندگان
چکیده
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. We determine the fair price of such options in a multidimensional Black-Scholes model which results in the computation of a multidimensional integral whose dimension equals the dimension of the underlying Brownian motion. 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, performancedependent options can efficiently be priced as it is shown by numerical results.
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