In this paper, a new numerical method based on adaptive gradient descent optimizers is provided for computing the implied volatility from the Black-Scholes (B-S) option pricing model. It is shown that the new method is more accurate than the close form approximation. Compared with the Newton-Raphson method, the new method obtains a reliable rate of convergence and tends to be less sensitive to the beginning point.

翻译：本文提供了一种基于适应性梯度下沉优化器的新的数字方法,用于计算黑雪(B-S)备选定价模式中隐含的波动性。 这表明新方法比近似形式更准确。 与牛顿-拉夫森方法相比,新方法获得了可靠的趋同率,往往对起始点不太敏感。