On the approximation of the Black and Scholes call function

The Black and Scholes call function is widely used for pricing and hedging. In this paper we present a new global approximating formula for the Black and Scholes call function that can be useful for deriving the risk of options i.e. the implied volatility. Lastly we compare, by numerical tests, our results with some popular methods available in literature (which are generally local) and we show, through Monte Carlo analysis, the computation error for extreme cases of both volatility and moneyness.