# Adaptive Gradient Descent Methods for Computing Implied Volatility

**Authors:** Yixiao Lu, Yihong Wang, Tinggan Yang  
**arXiv:** [2108.07035](https://arxiv.org/abs/2108.07035)  
**Date:** 2021-08-16  
**Summary page:** https://www.summarizepaper.com/en/paper/2108.07035v5/

## 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.