Analytical Study of Soliton Solutions and Modulation Instability Analysis in the M-Truncated Fractional Coupled Ivancevic Option-Pricing Model
Year: 2025
Type: article
Abstract: This work investigates the coupled Ivancevic option-pricing model, a nonlinear wave alternative to the Black–Scholes model. By utilizing the recently developed Kumar-Malik method, modified Sardar sub-equation method and the generalized Arnous method, the substantial results of this research are the successful derivation of novel exact soliton solutions, including bright, singular, dark, combined dark–bright, singular-periodic, complex solitons, exponential and Jacobi elliptic functions. A detailed analysis of option price wave functions and modulation instability analysis is conducted, with the conditions for valid solutions outlined. Additionally, a mathematical framework is established to capture market price fluctuations. Numerical simulations, illustrated through 2D, 3D and contour graphs, highlight the effects of parameter variations. Our findings demonstrate the effectiveness of the coupled Ivancevic model as a fractional nonlinear wave system, providing valuable insights into stock volatility and returns. This study contributes to creating new option-pricing models, which affect financial market analysis and risk management.
Source: Fractal and Fractional
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
OpenAlex ID: W4414593280