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In exponential semi-martingale setting for risky asset we estimate thedifference of prices of options when initial physical measure $P$ andcorresponding martingale measure $Q$ change to $\tilde{P}$ and $\tilde{Q}$respectively. Then, we estimate $L_1$-distance of option's prices forcorresponding parametric models with known and estimated parameters. Theresults are applied to exponential Levy models with special choice ofmartingale measure as Esscher measure, minimal entropy measure and$f^q$-minimal martingale measure. We illustrate our results by considering GMYand CGMY models.

On the stability of call/put option's prices in incomplete models under statistical estimations