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Optimal Algebras and Novel Solutions of Time‐Fractional (2 + 1) − D European Call Option Model

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  • Gimnitz Simon S.
  • B. Bira
  • Sathiyaraj Thambiayya

Abstract

In this article, we analyse the time‐fractional (2 + 1) − D Black–Scholes model for European call options by employing Lie symmetry analysis. We derive the infinitesimal transformations and classify the optimal systems. Furthermore, under the geometric Brownian motion, we reduced the given model to ordinary differential equation (ODE) with integer order. We have obtained different ODEs for different correlation values. Then, we construct the power series solutions and established its convergence. Furthermore, the reduced ODE is simulated numerically and the solutions are illustrated graphically. Finally, we explicitly find the conserved vectors.

Suggested Citation

  • Gimnitz Simon S. & B. Bira & Sathiyaraj Thambiayya, 2025. "Optimal Algebras and Novel Solutions of Time‐Fractional (2 + 1) − D European Call Option Model," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnddns:v:2025:y:2025:i:1:n:5568285
    DOI: 10.1155/ddns/5568285
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    1. Jian-Gen Liu & Yu-Feng Zhang & Jing-Jing Wang, 2023. "Investigation Of The Time Fractional Generalized (2 + 1)-Dimensional Zakharov–Kuznetsov Equation With Single-Power Law Nonlinearity," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-14.
    2. Lauterbach, Beni & Schultz, Paul, 1990. "Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives," Journal of Finance, American Finance Association, vol. 45(4), pages 1181-1209, September.
    3. Yu, Jicheng & Feng, Yuqiang, 2024. "On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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