Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding
Mathematical Finance
2024-10-04 v2 Computational Finance
Pricing of Securities
Abstract
Using the option delta systematically, we derive tighter lower and upper bounds of the Black-Scholes implied volatility than those in Tehranchi [SIAM J. Financ. Math. 7 (2016), 893-916]. As an application, we propose a Newton-Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton-Raphson algorithm, whose convergence is slow for extreme option prices.
Cite
@article{arxiv.2302.08758,
title = {Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding},
author = {Jaehyuk Choi and Jeonggyu Huh and Nan Su},
journal= {arXiv preprint arXiv:2302.08758},
year = {2024}
}