  In this paper we introduce the concept of standardized call function and we
obtain a new approximating formula for the Black and Scholes call function
through the hyperbolic tangent. This formula is useful for pricing and risk
management as well as for extracting the implied volatility from quoted
options. The latter is of particular importance since it indicates the risk of
the underlying and it is the main component of the option's price. Further we
estimate numerically the approximating error of the suggested solution and, by
comparing our results in computing the implied volatility with the most common
methods available in literature we discuss the challenges of this approach.
