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Arbitrage Problems with Reflected Geometric Brownian Motion

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  • Dean Buckner
  • Kevin Dowd
  • Hardy Hulley

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 num\'eraire portfolios or equivalent risk-neutral probability measures, which makes them totally unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate textbook no-arbitrage bounds.

Suggested Citation

  • Dean Buckner & Kevin Dowd & Hardy Hulley, 2022. "Arbitrage Problems with Reflected Geometric Brownian Motion," Papers 2201.05312, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2201.05312
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    References listed on IDEAS

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    Cited by:

    1. R. Guy Thomas, 2023. "Long-term option pricing with a lower reflecting barrier," Papers 2302.05808, arXiv.org.

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