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Methods for Analytical Barrier Option Pricing with Multiple Exponential Time-Varying Boundaries

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Abstract

We develop novel methods for efficient analytical solution of all types of partial time barrier options with both single and double exponential and time varying boundaries, and specifically to treat forward-starting partial double barrier options, which present the simplest non-trivial example of the multiple exponential time-varying barrier case. Our methods reduce the pricing of all barrier options with time-varying boundaries to the pricing of a single European option. We express our novel results solely in terms of European first and second order Gap options. We are motivated by similar structures appearing in Structural Credit Risk models for firm default.

Suggested Citation

  • Otto Konstandatos, 2018. "Methods for Analytical Barrier Option Pricing with Multiple Exponential Time-Varying Boundaries," Research Paper Series 396, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:396
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    File URL: https://www.uts.edu.au/sites/default/files/article/downloads/rp396.pdf
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    Cited by:

    1. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear double barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(1), pages 125-151, January.
    2. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo & Lee, Minha, 2023. "Pricing multi-step double barrier options by the efficient non-crossing probability," Finance Research Letters, Elsevier, vol. 54(C).

    More about this item

    Keywords

    Exotic Options; Method of Images; Partial Time Double Barrier Options; Window Double Barrier Options; Partial-time barrier options; Credit Risk;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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