Adaptive Gradient Descent Methods for Computing Implied Volatility

Abstract

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.

Our implement of Newton-Raphson iteration has defects. After correcting the code implement, we find Newton-Raphson won't be non-convergent. See https://github.com/cloudy-sfu/Newton-Raphson-Implied-Volatility for details

References in corpus (3)

• An overview of gradient descent optimization algorithms
• AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients
• A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks