On the Approximation of the Black and Scholes Call Function

Giuseppe Orlando and Giovanni Taglialatela, On the approximation of the Black and Scholes call function, Journal of Computational and Applied Mathematics, 28 August 2020, https://www.sciencedirect.com/science/article/abs/pii/S0377042720304453

Posted: 9 Nov 2020

See all articles by Giuseppe Orlando

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: August 28, 2020

Abstract

The Black and Scholes call function is widely used for pricing and hedging. In this paper we present a new global approximating formula for the Black and Scholes call function that can be useful for deriving the risk of options i.e. the implied volatility. Lastly we compare, by numerical test, our results with some popular methods available in literature (which are generally local) and we show, through Monte Carlo analysis, the computation error for extreme cases of both volatility and moneyness.

Keywords: Black and Scholes model, Hyperbolic tangent, Implied volatility, Inverse problem

JEL Classification: G10, C02, C88

Suggested Citation

Orlando, Giuseppe and Taglialatela, Giovanni, On the Approximation of the Black and Scholes Call Function (August 28, 2020). Giuseppe Orlando and Giovanni Taglialatela, On the approximation of the Black and Scholes call function, Journal of Computational and Applied Mathematics, 28 August 2020, https://www.sciencedirect.com/science/article/abs/pii/S0377042720304453, Available at SSRN: https://ssrn.com/abstract=3686976

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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