Challenges in Approximating the Black and Scholes Call Formula with Hyperbolic Tangents

Mininni, M., Orlando, G. & Taglialatela, G. Challenges in approximating the Black and Scholes call formula with hyperbolic tangents. Decisions Econ Finan (2020). https://doi.org/10.1007/s10203-020-00305-8

Posted: 9 Nov 2020

See all articles by Michele Mininni

Michele Mininni

Università degli Studi di Bari “Aldo Moro” (UNIBA)

Giuseppe Orlando

Università degli Studi di Bari “Aldo Moro” (UNIBA) - Department of Economics and Mathematical Methods; Università degli Studi di Camerino - School of Science and Technologies

Giovanni Taglialatela

Università degli Studi di Bari “Aldo Moro” (UNIBA) - Dipartimento di Economia e Finanza

Date Written: September 13, 2020

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: Option Pricing, Black and Scholes, Hyperbolic Tangent

JEL Classification: G10, C02, G12

Suggested Citation

Mininni, Michele and Orlando, Giuseppe and Taglialatela, Giovanni, Challenges in Approximating the Black and Scholes Call Formula with Hyperbolic Tangents (September 13, 2020). Mininni, M., Orlando, G. & Taglialatela, G. Challenges in approximating the Black and Scholes call formula with hyperbolic tangents. Decisions Econ Finan (2020). https://doi.org/10.1007/s10203-020-00305-8, Available at SSRN: https://ssrn.com/abstract=3696112

Michele Mininni

Università degli Studi di Bari “Aldo Moro” (UNIBA) ( email )

Piazza Umberto I
Bari, 70121
Italy

Giuseppe Orlando (Contact Author)

Università degli Studi di Bari “Aldo Moro” (UNIBA) - Department of Economics and Mathematical Methods ( email )

Via C. Rosalba 53
VI Floor, Room 12
Bari, 70124
Italy
+39 080 5049218 (Phone)

Università degli Studi di Camerino - School of Science and Technologies ( email )

Via M. delle Carceri 9
Camerino, 62032
Italy

Giovanni Taglialatela

Università degli Studi di Bari “Aldo Moro” (UNIBA) - Dipartimento di Economia e Finanza ( email )

Piazza Umberto I
Bari, 70121
Italy

HOME PAGE: http://https://www.uniba.it/docenti/taglialatela-giovanni

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