Black–Scholes equation in quantitative finance with variable parameters: a path to a generalized Sch скачать в хорошем качестве

Black–Scholes equation in quantitative finance with variable parameters: a path to a generalized Sch

This research introduces a refined Black–Scholes model designed to better reflect the fluid nature of modern financial markets. By replacing static variables with time-varying parameters governed by power law dynamics, the authors address the traditional framework's failure to account for shifting volatility and interest rates. The study utilizes advanced mathematical tools, such as Laplace transforms and Wick rotations, to derive analytical solutions for derivative pricing. Furthermore, the paper establishes a unique connection between quantum physics and quantitative finance, comparing stock price movements to particle behavior through a quantum-mechanical lens. Numerical simulations reveal that this generalized approach produces wave-like solitary solutions that align more closely with empirical market data. Consequently, this work offers a robust theoretical improvement for forecasting option values in increasingly complex economic environments. R. A. El-Nabulsi, W. Anukool, “Black-Scholes Equation in Quantitative Finance with Variable Parameters: A Path to a Generalized Schrodinger Equation,” Financial Innovation, 2026. https://doi.org/10.1186/s40854-025-00...