Analytical valuation of options on joint minima and maxima

Tristan Guillaume ()
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Tristan Guillaume: THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper, we show how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, we give formulae for standard step-up and step-down barrier options, as well as partial and outside step-up and step-down barrier options, involving multiple integrals of dimensions ranging between three and five. Our 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: option; barrier; step barrier; pricing; dimension (search for similar items in EconPapers)
Date: 2002
Note: View the original document on HAL open archive server: https://hal.science/hal-00924237
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Published in Applied Mathematical Finance, 2002, 8 (4), pp.209-235

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