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Rainbow Step Barrier Options

Author

Listed:
  • Tristan Guillaume

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

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.

Suggested Citation

  • Tristan Guillaume, 2024. "Rainbow Step Barrier Options," JRFM, MDPI, vol. 17(8), pages 1-32, August.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:8:p:356-:d:1455608
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    References listed on IDEAS

    as
    1. Tristan Guillaume, 2015. "On the Computation of the Survival Probability of Brownian motion with Drift in a Closed Time Interval when the Absorbing Boundary is a Step Function," Post-Print hal-02979986, HAL.
    2. Tristan Guillaume, 2015. "On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-22, September.
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