valuation of options on joint minima and maxima

Tristan Guillaume

Applied Mathematical Finance, 2001, vol. 8, issue 4, 209-233

Abstract: It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation.

Keywords: Dimensionality; Joint Extrema; Step Barrier Options; Quasi-RANDOM Integration (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1080/13504860210122384

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