An empirical study on using Hurst exponent estimation methods for pricing Call options by fractional Black–Scholes model

Issue title: Fractional Calculus and Its Applications

Guest editors: Sergio Bianchi

Article type: Research Article

Authors: Kilianová, Soňa^{; *} | Letko, Boris

Affiliations: Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia

Correspondence: [*] Corresponding author. E-mail: sona.kilianova@fmph.uniba.sk.

Abstract: This paper is an empirical study investigating the effect of using a fractional Black–Scholes model for pricing Call options in comparison to the classical Black–Scholes model. We estimate the Hurst parameter by nine different methods available in software R, for a set of fifteen assets from four different industries and for various lengths of used historical data. We use implied volatility for calculation of option price with a one month time to maturity. As a main result, we provide a table of tendencies of suitability for using each of the Hurst exponent estimation methods depending on the length of underlying data set.

Keywords: Call option, fractional Black–Scholes model, fractional Brownian motion, Hurst exponent

DOI: 10.3233/RDA-180137

Journal: Risk and Decision Analysis, vol. 7, no. 1-2, pp. 51-62, 2018