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Arbitrage problems with reflected geometric Brownian motion

Author

Listed:
  • Dean Buckner

    (The Eumaeus Project)

  • Kevin Dowd

    (Durham University Business School)

  • Hardy Hulley

    (University of Technology Sydney)

Abstract

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numéraire portfolios or equivalent risk-neutral probability measures, which makes them unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

Suggested Citation

  • Dean Buckner & Kevin Dowd & Hardy Hulley, 2024. "Arbitrage problems with reflected geometric Brownian motion," Finance and Stochastics, Springer, vol. 28(1), pages 1-26, January.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:1:d:10.1007_s00780-023-00525-x
    DOI: 10.1007/s00780-023-00525-x
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    Cited by:

    1. Alexis Anagnostakis & David Criens & Mikhail Urusov, 2025. "On weak notions of no-arbitrage in a 1D general diffusion market with interest rates," Papers 2503.14078, arXiv.org.

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    More about this item

    Keywords

    Reflected geometric Brownian motion; Arbitrage; Local time; Contingent claim valuation;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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