Arbitrage problems with reflected geometric Brownian motion

Dean Buckner (), Kevin Dowd () and Hardy Hulley ()
Additional contact information
Dean Buckner: The Eumaeus Project
Kevin Dowd: Durham University Business School
Hardy Hulley: University of Technology Sydney

Finance and Stochastics, 2024, vol. 28, issue 1, No 1, 26 pages

Abstract: 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.

Keywords: Reflected geometric Brownian motion; Arbitrage; Local time; Contingent claim valuation; 60H10; 91G15; 91G16 (search for similar items in EconPapers)
JEL-codes: C6 G12 G13 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-023-00525-x

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