In this short notice some comments on local volatility are provided. The Black–Scholes (BS) model of the options pricing has advised a ‘fair’ price that interpreted as the PV of the ‘neutralized’ pay off value at maturity. In BS equation (BSE) the real stock return μ is replaced by the risk-free rate of return r. These parameters are assumed to be constants though the setting admits that μ, r, and volatility σ could be known deterministic functions on time t. If the market option prices are given one could calculate volatility of the underlying. This calculation leads to a notion known as implied volatility. If the model and calculation are perfect, this implied volatility value would be the same for the options with different strike prices and maturities. In reality the calculations show that this is not the case. Implied Black–Scholes volatilities highlight a strong dependence on maturity T and the strike price K. The dependence of the implied volatility on K and T is known as “smile” effect. The way how to solve the smile problem was presented in [1-3]. We briefly recall following [1] the main steps of this derivation. The riskneutral stock price in the BS model is assumed to be written in the form