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Perpetual Dual American Barrier Options for Short Sellers

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Stochastic Models, Statistics and Their Applications (SMSA 2019)

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Abstract

We obtain closed-form solutions to the problems of pricing of perpetual American put and call barrier options in the one-dimensional Black–Merton–Scholes model from the point of view of short sellers. The proof is based on the reduction of the original optimal stopping problems for a one-dimensional geometric Brownian motion with positive exponential discounting rates to the equivalent free-boundary problems and the solution of the latter problems by means of the smooth-fit conditions.

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Acknowledgements

The author is grateful to an anonymous Referee for their careful reading of the manuscript and helpful suggestions, which allowed to improve the presentation of the paper. This research was supported by a Small Grant from the Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD) at the London School of Economics and Political Science.

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Authors and Affiliations

  1. Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    Pavel V. Gapeev

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  1. Pavel V. Gapeev
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Correspondence to Pavel V. Gapeev .

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Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Department of Control Systems and Mechatronics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Institute of Transport and Economics, Technische Universität Dresden, Dresden, Germany

    Ostap Okhrin

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Gapeev, P.V. (2019). Perpetual Dual American Barrier Options for Short Sellers. In: Steland, A., Rafajłowicz, E., Okhrin, O. (eds) Stochastic Models, Statistics and Their Applications. SMSA 2019. Springer Proceedings in Mathematics & Statistics, vol 294. Springer, Cham. https://doi.org/10.1007/978-3-030-28665-1_6

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