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In this paper we introduce the concept of standardized call function and weobtain a new approximating formula for the Black and Scholes call functionthrough the hyperbolic tangent. This formula is useful for pricing and riskmanagement as well as for extracting the implied volatility from quotedoptions. The latter is of particular importance since it indicates the risk ofthe underlying and it is the main component of the option's price. Further weestimate numerically the approximating error of the suggested solution and, bycomparing our results in computing the implied volatility with the most commonmethods available in literature we discuss the challenges of this approach.

Challenges in approximating the Black and Scholes call formula with hyperbolic tangents