Paper: arXiv 2601.00293

Authors: Pengpeng Li, Shi-Dong Liang

Abstract

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can take various unexpected market behaviors into account to modify the option pricing. As examples, we present several market forces to analyze their effects on the option pricing. These results provide us two practical applications. One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging. The other implies the existence of some risk premium when some unexpected forces emerge.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a theoretical framework mapping quantum harmonic oscillators and Schrödinger equations to option pricing under non-Gaussian market forces. However, it completely lacks empirical validation, backtesting on historical market data, or quantitative comparison to real option prices.

Research Flowchart

  flowchart TD
    A["Research Goal: Generalize Black-Scholes Model via Quantum Mechanics"] --> B["Analogy: Stochastic Dynamics to Quantum Harmonic Oscillator"]
    C["Inputs: Market Data & Potential External Market Forces"] --> D["Computational Process: Formulate Quantum-Based Pricing Model"]
    B --> D
    D --> E["Derive Modified Option Pricing Schemes"]
    E --> F["Outcomes: New Pricing Model for Predicted Forces & Identified Risk Premiums"]

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0 of 27 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.