Option Pricing beyond Black-Scholes Model: Quantum Mechanics Approach

Battle Count: 102

The paper provides a novel theoretical framework for modifying Black-Scholes option pricing to account for non-Gaussian market dynamics driven by hidden forces (shorting, buying, news, psychological effects). While intellectually interesting and potentially useful for exotic option pricing and risk premium estimation, it lacks empirical validation, calibration procedures, and practical implementation guidance. The relevance is primarily at the theoretical/modeling level rather than at the execution or strategy level. A quantitative trader would need significant additional work to calibrate the force parameters and integrate this into a trading system.

Implementation requires: (1) solving the time-independent Schrödinger equation for various potentials (analytically for simple cases, numerically for complex ones), (2) applying perturbation theory for higher-order forces, (3) computing the modified probability density and effective volatility, (4) integrating the modified distribution into the Black-Scholes pricing formula. The mathematical background in quantum mechanics (creation/annihilation operators, Hermite polynomials, perturbation theory) is substantial. For the constant and linear force cases, closed-form solutions exist. For x² and x³ forces, perturbation expansions are needed. The quantum well case requires solving a boundary-value problem. No code is provided.

The paper provides complete analytical derivations (Eqs. 1-49) and specifies numerical parameters (r=10%, S₀=20, K=20, T=1 year, σ=25%) for all figures. However, no code, no dataset, and no step-by-step computational scripts are provided. Reproduction requires solving the Schrödinger equation and performing perturbation calculations manually or with symbolic/numerical tools. The appendices contain detailed derivations for the perturbation method, aiding reproducibility.