A Generalized Derivation of The Black-Scholes Implied Volatility Through Hyperbolic Tangents

• Autorzy: Michele Mininni , Giuseppe Orlando , Giovanni Taglialatela
• Języki publikacji: EN

Abstrakty

EN

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 Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to derive the implied volatility of options.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

Słowa kluczowe

PL

Model Blacka-Scholesa; Rynek; Instrumenty finansowe; Dynamika cen

EN

Black-Scholes model; Market; Financial instruments; Price dynamics

• Czasopismo: Argumenta Oeconomica
• Rocznik: 2022
• Numer: nr 2 (49)
• Strony: 23-57

Twórcy

autor

Michele Mininni

• Department of Economics and Finance, Università degli Studi di Bari "Aldo Moro", Bari, Italy.

autor

Giuseppe Orlando

• Department of Economics and Finance, Università degli Studi di Bari "Aldo Moro", Bari, Italy.

autor

Giovanni Taglialatela

• Department of Economics and Finance, Università degli Studi di Bari "Aldo Moro", Bari, Italy.

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Identyfikatory

DOI

10.15611/aoe.2022.2.02