English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper a time-fractional Black-Scholes model (TFBSM) is considered tostudy the price change of the underlying fractal transmission system. Wedevelop and analyze a numerical method to solve the TFBSM governing Europeanoptions. The numerical method combines the exponential B-spline collocation todiscretize in space and a finite difference method to discretize in time. Themethod is shown to be unconditionally stable using von-Neumann analysis. Also,the method is proved to be convergent of order two in space and $2-\mu$ istime, where $\mu$ is order of the fractional derivative. We implement themethod on various numerical examples in order to illustrate the accuracy of themethod, and validation of the theoretical findings. In addition, as anapplication, the method is used to price several different European optionssuch as the European call option, European put option, and European doublebarrier knock-out call option.

An efficient numerical method based on exponential B-splines for time-fractional Black-Scholes equation governing European options