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

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

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.

Suggested Citation

  • Al–Zhour, Zeyad & Barfeie, Mahdiar & Soleymani, Fazlollah & Tohidi, Emran, 2019. "A computational method to price with transaction costs under the nonlinear Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 291-301.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:291-301
    DOI: 10.1016/j.chaos.2019.06.033
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    References listed on IDEAS

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    Cited by:

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    2. Lyu, Jisang & Park, Eunchae & Kim, Sangkwon & Lee, Wonjin & Lee, Chaeyoung & Yoon, Sungha & Park, Jintae & Kim, Junseok, 2021. "Optimal non-uniform finite difference grids for the Black–Scholes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 690-704.
    3. Bahareh Afhami & Mohsen Rezapour & Mohsen Madadi & Vahed Maroufy, 2021. "Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk," Papers 2104.11594, arXiv.org.
    4. Zhang, Ruixiaoxiao & Shimada, Koji & Ni, Meng & Shen, Geoffrey Q.P. & Wong, Johnny K.W., 2020. "Low or No subsidy? Proposing a regional power grid based wind power feed-in tariff benchmark price mechanism in China," Energy Policy, Elsevier, vol. 146(C).

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