Adaptive Gradient Descent Methods for Computing Implied Volatility

TL;DR

This paper introduces an adaptive gradient descent approach for calculating implied volatility in the Black-Scholes model, demonstrating improved accuracy and convergence reliability over traditional methods.

Contribution

The paper presents a novel adaptive gradient descent algorithm specifically designed for implied volatility computation, outperforming existing methods in accuracy and stability.

Findings

More accurate than close form approximation

Reliable convergence rate

Less sensitive to initial guesses

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.