Challenges in approximating the Black and Scholes call formula with hyperbolic tangents

Michele Mininni (), Giuseppe Orlando and Giovanni Taglialatela ()
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Michele Mininni: Università degli Studi di Bari “Aldo Moro”
Giovanni Taglialatela: Università degli Studi di Bari “Aldo Moro”

Decisions in Economics and Finance, 2021, vol. 44, issue 1, No 6, 73-100

Abstract: Abstract In this paper, we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. Differently from other solutions proposed in the literature, this formula is invertible; hence, it is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option’s price. That is what trading desks focus on. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common methods available in the literature, we discuss the challenges of this approach.

Keywords: Black and Scholes model; Hyperbolic tangent; Implied volatility; 65-02; 91G20; 91G60 (search for similar items in EconPapers)
JEL-codes: C02 C88 G10 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Working Paper: Challenges in approximating the Black and Scholes call formula with hyperbolic tangents (2018)
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DOI: 10.1007/s10203-020-00305-8

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