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Valuation of Performance-Dependent Options

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  • Thomas Gerstner
  • Markus Holtz

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 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, a pricing formula is derived 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 is shown by numerical results.

Suggested Citation

  • Thomas Gerstner & Markus Holtz, 2008. "Valuation of Performance-Dependent Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(1), pages 1-20.
    • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:1:p:1-20
    DOI: 10.1080/13504860601170492
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    Cited by:

    1. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.

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