Tighter 'uniform bounds for Black-Scholes implied volatility' and the applications to root-finding

Jaehyuk Choi, Jeonggyu Huh and Nan Su

Papers from arXiv.org

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.

Date: 2023-02, Revised 2024-10
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Published in Operations Research Letters, 57:107189, 2024

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