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

12 Pages Posted: 18 Nov 2018

See all articles by Michele Mininni

Michele Mininni

University of Bari

Giuseppe Orlando

University of Bari - Department of Economics and Mathematical Methods; Università degli Studi di Camerino - School of Science and Technologies

Giovanni Taglialatela

University of Bari - Dipartimento di Economia e Finanza; University of Bari - Department of Economics and Mathematical Methods

Date Written: September 20, 2018

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. This formula 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. 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 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 20, 2018). Available at SSRN: https://ssrn.com/abstract=3266556 or http://dx.doi.org/10.2139/ssrn.3266556

Michele Mininni

University of Bari ( email )

Piazza Umberto I
Bari, 70121
Italy

Giuseppe Orlando (Contact Author)

University of Bari - 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

University of Bari - Dipartimento di Economia e Finanza ( email )

Piazza Umberto I
Bari, 70121
Italy

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

University of Bari - Department of Economics and Mathematical Methods ( email )

Largo Abbey St. Scholastica
Bari, 70124
Italy

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

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