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Model uncertainty in option pricing: challenging the Black-Scholes formula

Abstract
It is well known that the validity of the Black-Scholes (BS) 
formula is restricted to the case, when the Market model is a geometric 
Brownian motion and therefore admits only one Martingale measure.
We consider the situation, when the decision is made on the basis of an 
acceptability measure (the dual of a risk measure) and the market model 
is not exactly known, but it is known that it belongs to some ambiguity 
set of models. We demonstrate that in this case a nonzero bid-ask 
spread appears, even if the market model is close to the BS model.
The bid-ask spread increases with the degree of model uncertainty, but 
decreases with the acceptability level.

The results are based on a duality theorem for ambiguous decisions.

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