A computational method to price with transaction costs under the nonlinear Black–Scholes model

Al–Zhour, Zeyad, Mahdiar Barfeie, Fazlollah Soleymani and Emran Tohidi

Chaos, Solitons & Fractals, 2019, vol. 127, issue C, 291-301

Abstract: More realistic models in option pricing are based on nonlinear modifications of the well–known Black–Scholes PDE due to considering other factors such as transaction costs and risks from an unprotected portfolio. The aim of this research is to price a nonlinear volatility model. The new approach leads to sparse matrices of second order of convergence after a special semi–discretization. The resulting system of equations is time–varying. Accordingly, an implicit time–stepping method is applied with quadratical accuracy, which is not as step–size sensitive as the commonly–used explicit ones. It is discussed that under what conditions the overall scheme is time–stable. Numerical results are given to verify the robustness and usefulness of our method in contrast to the commonly–used methods of the literature for this task.

Keywords: Nonlinear Black–Scholes equation; Non–uniform grid; Option pricing; Transaction costs; Time–varying system. (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:127:y:2019:i:c:p:291-301

DOI: 10.1016/j.chaos.2019.06.033

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