https://doi.org/10.1140/epjp/s13360-024-05435-1
Regular Article
The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model
1
IT4 Innovations, VŠB - Technical University of Ostrava, 70800, Poruba-Ostrava, Czech Republic
2
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia
Received:
24
June
2024
Accepted:
6
July
2024
Published online:
26
July
2024
In this study, the coupled nonlinear volatility and option pricing model is examined. A leverage effect is produced, indicating a negative correlation between stock returns and volatility, and a confined Brownian motion linked to the nonlinear Schrödinger equation is exhibited. This model is considered a coupled nonlinear wave substitute for the Black-Scholes option pricing model. A mathematical strategy is introduced to comprehend market price fluctuations for the suggested model. Consequently, the necessary parameters for the existence of these solutions are revealed. The obtained numerical results of market price are discussed through graphs to illustrate and validate the theoretical findings. The generalized mapping approach of Riccati equations is applied to the model under consideration. Several periodic and singular soliton solutions are successfully constructed for the model. When appropriate parameters are chosen, both 2- and 3-dimensional plots that graphically represent some of the observed waveform solutions are included. Additionally, bifurcation, chaotic analysis, Lyapunov exponents, and multi-stability are performed to gain deeper insights into the related dynamical system. Phase portraits of market price fluctuations are shown for various parametric values of the corresponding dynamical system and at the equilibrium points. The results demonstrate that slight changes in initial conditions lead to price fluctuations in the model.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
