A generalized derivation of the Black-Scholes implied volatility through hyperbolic tangents
-
Published:2022
Issue:2
Volume:2022
Page:23-57
-
ISSN:1233-5835
-
Container-title:Argumenta Oeconomica
-
language:en
-
Short-container-title:Argumenta Oeconomica
Author:
Mininni Michele,Orlando Giuseppe,Tagliatela Giovanni
Abstract
This article extends the previous research on the notion of a standardized call function and how to obtain an approximate model of the Black-Scholes formula via the hyperbolic tangent. Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to derive the implied volatility of options. This is particularly important for traders because it represents the risk of the underlying, and is the main factor in the option price. The approximation error of the suggested solution was estimated and the results compared with the most common methods available in the literature. A new formula was provided to correct some cases of underestimation of implied volatility. Graphic evidence, stress tests and Monte Carlo analysis confirm the quality of the results obtained. Finally, further literature is provided as to why implied volatility is used in decision making.
Publisher
Wroclaw University of Economics and Business
Subject
Strategy and Management,Economics and Econometrics
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Russian nuclear weapons, 2023;Bulletin of the Atomic Scientists;2023-05-04