Arbitrage problems with reflected geometric Brownian motion. (English) Zbl 1530.91544
Summary: 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.
MSC:
| 91G15 | Financial markets |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
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