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

Gimnitz Simon S., B. Bira and Sathiyaraj Thambiayya

Discrete Dynamics in Nature and Society, 2025, vol. 2025, 1-11

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:5568285

DOI: 10.1155/ddns/5568285

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