Coupled transform method for time-space fractional Black-Scholes option pricing model

Coupled transform method for time-space fractional Black-Scholes option pricing model

This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The conside...

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Main Authors: S.O. Edeki, R.M. Jena, S. Chakraverty, D. Baleanu
Format: Article
Language:English
Published: Elsevier 2020-10-01
Series:Alexandria Engineering Journal
Subjects:
Option pricing
Black Scholes model
RDTM
Fractional derivative
Analytical solutions
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016820304087
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spelling doaj-2d7b2896067a4e908806996dd30405a62021-06-02T15:57:09ZengElsevierAlexandria Engineering Journal1110-01682020-10-0159532393246Coupled transform method for time-space fractional Black-Scholes option pricing modelS.O. Edeki0R.M. Jena1S. Chakraverty2D. Baleanu3Department of Mathematics, Covenant University, Ota, Nigeria; Corresponding author.Department of Mathematics, National Institute of Technology, Rourkela, IndiaDepartment of Mathematics, National Institute of Technology, Rourkela, IndiaDepartment of Mathematics, Faculty of Art and Sciences, Cankaya University, Balgat, 06530 Ankara, Turkey; Institute of Space Sciences, 077125 Magurele-Bucharest, RomaniaThis paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The considered cases and applications show more consistency of the TSFBSM with an actual integer and fractional data when compared with the classical Black-Scholes model. The method is noted to be very effective, even with little knowledge of fractional calculus. Extension of this to multi-factor models formulated in terms of stochastic dynamics is highly recommended.http://www.sciencedirect.com/science/article/pii/S1110016820304087Option pricingBlack Scholes modelRDTMFractional derivativeAnalytical solutions
collection DOAJ
language English
format Article
sources DOAJ
author S.O. Edeki
R.M. Jena
S. Chakraverty
D. Baleanu
spellingShingle S.O. Edeki
R.M. Jena
S. Chakraverty
D. Baleanu
Coupled transform method for time-space fractional Black-Scholes option pricing model
Alexandria Engineering Journal
Option pricing
Black Scholes model
RDTM
Fractional derivative
Analytical solutions
author_facet S.O. Edeki
R.M. Jena
S. Chakraverty
D. Baleanu
author_sort S.O. Edeki
title Coupled transform method for time-space fractional Black-Scholes option pricing model
title_short Coupled transform method for time-space fractional Black-Scholes option pricing model
title_full Coupled transform method for time-space fractional Black-Scholes option pricing model
title_fullStr Coupled transform method for time-space fractional Black-Scholes option pricing model
title_full_unstemmed Coupled transform method for time-space fractional Black-Scholes option pricing model
title_sort coupled transform method for time-space fractional black-scholes option pricing model
publisher Elsevier
series Alexandria Engineering Journal
issn 1110-0168
publishDate 2020-10-01
description This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The considered cases and applications show more consistency of the TSFBSM with an actual integer and fractional data when compared with the classical Black-Scholes model. The method is noted to be very effective, even with little knowledge of fractional calculus. Extension of this to multi-factor models formulated in terms of stochastic dynamics is highly recommended.
topic Option pricing
Black Scholes model
RDTM
Fractional derivative
Analytical solutions
url http://www.sciencedirect.com/science/article/pii/S1110016820304087
work_keys_str_mv AT soedeki coupledtransformmethodfortimespacefractionalblackscholesoptionpricingmodel
AT rmjena coupledtransformmethodfortimespacefractionalblackscholesoptionpricingmodel
AT schakraverty coupledtransformmethodfortimespacefractionalblackscholesoptionpricingmodel
AT dbaleanu coupledtransformmethodfortimespacefractionalblackscholesoptionpricingmodel
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