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A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets

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  • Company, Rafael
  • Jódar, Lucas
  • Pintos, José-Ramón

Abstract

Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black–Scholes problem. Nonlinear models appear when transaction costs or illiquid market effects are taken into account. This paper deals with the numerical analysis of nonlinear Black–Scholes equations modeling illiquid markets when price impact in the underlying asset market affects the replication of a European contingent claim. Numerical analysis of a nonlinear model is necessary because disregarded computations may waste a good mathematical model. In this paper we propose a finite-difference numerical scheme that guarantees positivity of the solution as well as stability and consistency.

Suggested Citation

  • Company, Rafael & Jódar, Lucas & Pintos, José-Ramón, 2012. "A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1972-1985.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:10:p:1972-1985
    DOI: 10.1016/j.matcom.2010.04.026
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    References listed on IDEAS

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    1. Liu, Hong & Yong, Jiongmin, 2005. "Option pricing with an illiquid underlying asset market," Journal of Economic Dynamics and Control, Elsevier, vol. 29(12), pages 2125-2156, December.
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    Cited by:

    1. Riccardo Fazio, 2015. "A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Options," Papers 1504.04594, arXiv.org.
    2. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Manuel L. Esquível & Nadezhda P. Krasii & Pedro P. Mota & Victoria V. Shamraeva, 2023. "Coupled Price–Volume Equity Models with Auto-Induced Regime Switching," Risks, MDPI, vol. 11(11), pages 1-20, November.
    4. Ahmadian, D. & Farkhondeh Rouz, O. & Ivaz, K. & Safdari-Vaighani, A., 2020. "Robust numerical algorithm to the European option with illiquid markets," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    5. Karol Duris & Shih-Hau Tan & Choi-Hong Lai & Daniel Sevcovic, 2015. "Comparison of the analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations," Papers 1511.05661, arXiv.org, revised Nov 2015.

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