Rainbow Step Barrier Options

Tristan Guillaume ()
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Tristan Guillaume: Laboratoire Thema, CYU Cergy Paris Université, 33 Boulevard du Port, F-95011 Cergy-Pontoise Cedex, France

JRFM, 2024, vol. 17, issue 8, 1-32

Abstract: This article provides exact analytical formulae for various kinds of rainbow step barrier options. These are highly flexible and sophisticated multi-asset barrier options based on the following principle: the option life is divided into several time intervals on which different barriers are monitored w.r.t. different underlying assets. From a mathematical point of view, new results are provided for the first passage time of a multidimensional geometric Brownian motion to a boundary defined as a step function. The article shows how to implement the obtained option valuation formulae in a simple and very efficient manner. Numerical results highlight a strong sensitivity of rainbow step barrier options to the correlations between the underlying assets.

Keywords: rainbow step barrier option; rainbow option; step barrier option; barrier option; multiasset option; multiasset barrier option; first passage time; boundary crossing probability; multidimensional Brownian motion (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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