A robust numerical solution to a time-fractional Black–Scholes equation

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dc.contributor.authorNuugulu, S.M
dc.contributor.authorGideon, F
dc.contributor.authorPatidar, K.C
dc.date.accessioned2021-04-14T12:11:54Z
dc.date.available2021-04-14T12:11:54Z
dc.date.issued2021
dc.description.abstractDividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in which random fractional white noise has the potential to accurately estimate European put option premiums while providing a good numerical convergence. The aim of this paper is two fold: firstly, to construct a time-fractional (tfBS) PDE for pricing European options on continuous dividend paying stocks, and, secondly, to propose an implicit finite difference method for solving the constructed tfBS PDE. Through rigorous mathematical analysis it is established that the implicit finite difference scheme is unconditionally stable. To support these theoretical observations, two numerical examples are presented under the proposed fractional framework. Results indicate that the tfBS and its proposed numerical method are very effective mathematical tools for pricing European options.en_US
dc.identifier.citationNuugulu, S.M. et al. (2021). A robust numerical solution to a time-fractional Black–Scholes equation. Advances in Difference Equations 2021(1),123en_US
dc.identifier.issn16871839
dc.identifier.uri10.1186/s13662-021-03259-2
dc.identifier.urihttp://hdl.handle.net/10566/6021
dc.language.isoenen_US
dc.publisherSpringer Natureen_US
dc.subjectOption pricingen_US
dc.subjectTime-fractional Black–Scholes equationsen_US
dc.subjectFinite difference methodsen_US
dc.subjectConvergence and stability analysisen_US
dc.titleA robust numerical solution to a time-fractional Black–Scholes equationen_US
dc.typeArticleen_US

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