An efficient numerical method for pricing double-barrieroptions on an underlying stock governed by a fractal stochastic process

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dc.contributor.authorNuugulu, Samuel Megameno
dc.contributor.authorGideon, Frednard
dc.contributor.authorPatidar, Kailash C.
dc.date.accessioned2023-06-15T07:24:02Z
dc.date.available2023-06-15T07:24:02Z
dc.date.issued2023
dc.description.abstractAfter the discovery of the fractal structures of financial markets, enormous effort has been dedicated to finding accurate and stable numerical schemes to solve fractional Black-Scholes partial differential equations. This work, therefore, proposes a numerical scheme for pricing double-barrier options, written on an underlying stock whose dynamics are governed by a non-standard fractal stochastic process. The resultant model is time-fractional and is herein referred to as a time-fractional Black-Scholes model. The presence of the time-fractional derivative helps to capture the time-decaying effects of the underlying stock while capturing the globalized change in underlying prices and barriers. In this paper, we present the construction of the proposed scheme, analyse it in terms of its stability and convergence, and present two numerical examples of pricing double knock-in barrier-option problems. The results suggest that the proposed scheme is unconditionally stable and convergent with order O(h2 + k2).en_US
dc.identifier.urihttp://hdl.handle.net/11070/3706
dc.language.isoenen_US
dc.publisherMDPIen_US
dc.subjectTime-fractional Black-Scholes PDEsen_US
dc.subjectDouble barriers optionsen_US
dc.subjectNumerical methodsen_US
dc.titleAn efficient numerical method for pricing double-barrieroptions on an underlying stock governed by a fractal stochastic processen_US
dc.typeArticleen_US
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