Adaptive Gradient Descent Methods for Computing Implied Volatility

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.