Adaptive Gradient Descent Methods for Computing Implied Volatility
Computational Finance
2023-03-24 v5
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.
Keywords
Cite
@article{arxiv.2108.07035,
title = {Adaptive Gradient Descent Methods for Computing Implied Volatility},
author = {Yixiao Lu and Yihong Wang and Tinggan Yang},
journal= {arXiv preprint arXiv:2108.07035},
year = {2023}
}
Comments
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