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We study the risk premium impact in the Perturbative Black Scholes model. ThePerturbative Black Scholes model, developed by Scotti, is a subjectivevolatility model based on the classical Black Scholes one, where the volatilityused by the trader is an estimation of the market one and contains measurementerrors. In this article we analyze the correction to the pricing formulas dueto the presence of an underlying drift different from the risk free return. Weprove that, under some hypothesis on the parameters, if the asset price is asub-martingale under historical probability, then the implied volatilitypresents a skewed structure, and the position of the minimum depends on therisk premium $\lambda$.

Risk Premium Impact in the Perturbative Black Scholes Model