Title:

A generalized derivation of the Black-Scholes implied volatility through hyperbolic tangents

Group publication title:

Argumenta Oeconomica

Creator:

Mininni, Michele ; Orlando, Giuseppe ; Taglialatela, Giovanni

Subject and Keywords:

implied volatility ; approximation methods ; hyperbolic tangent ; Black-Scholes model

Description:

Argumenta Oeconomica, 2022, Nr 2 (49), s. 23-57

Abstrakt:

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 Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to derive the implied volatility of options.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:

Publishing House of Wroclaw University of Economics and Business

Place of publication:

Wroclaw

Date:

2022

Resource Type:

artykuł

Resource Identifier:

doi:10.15611/aoe.2022.2.02

Language:

eng

Relation:

Argumenta Oeconomica, 2022, Nr 2 (49)

Rights:

Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy

Access Rights:

Dla wszystkich zgodnie z licencją

License:

CC BY-SA 4.0

Location:

Uniwersytet Ekonomiczny we Wrocławiu