Article
Version 1
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Rainbow Step Barrier Options
Version 1
: Received: 20 June 2024 / Approved: 21 June 2024 / Online: 21 June 2024 (12:53:31 CEST)
How to cite: guillaume, T. Rainbow Step Barrier Options. Preprints 2024, 2024061530. https://doi.org/10.20944/preprints202406.1530.v1 guillaume, T. Rainbow Step Barrier Options. Preprints 2024, 2024061530. https://doi.org/10.20944/preprints202406.1530.v1
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 formulae 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 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
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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