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.

中文翻译：

---

关于Black和Scholes调用函数的逼近

Black and Scholes赎回函数被广泛用于定价和对冲。在本文中，我们为Black和Scholes调用函数提供了一个新的全局逼近公式，该公式可用于推导出期权的风险，即隐含波动率。最后，通过数值测试，我们将结果与文献中提供的一些流行方法（通常是本地方法）进行了比较，并通过蒙特卡洛分析显示了波动性和货币性极端情况下的计算误差。