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Quantum Leap: A Price Leap Mechanism in Financial Markets

Author

Listed:
  • Haoran Zheng

    (School of Economics, Shanghai University, Shanghai 200444, China)

  • Jing Bai

    (School of Economics, Shanghai University, Shanghai 200444, China)

Abstract

This study explores the quantum leapfrog mechanism within the context of quantum finance and presents a new interpretation of established financial models through a quantum perspective. In quantum physics, the well-documented phenomenon of particles tunneling through energy barriers has a parallel in finance. We propose a quantum financial leapfrog model in which asset prices make quantum leaps, penetrating market “energy barriers” in non-sequential advances. By leveraging the Hamiltonian operator and the Schrödinger equation, our approach simulates the dynamics of asset prices in a manner akin to the trajectories of particles in quantum mechanics. We draw an analogy between financial markets and gravitational fields, and from this we derive energy equations for pricing orbits. Using path integration techniques, we map out potential price transitions between these orbits, which are guided by the calculation of minimal energy barriers. Furthermore, we introduce a market “propagator” that aligns with the uncertainty principle, identifying the optimal price pathways. Our findings provide new insights and methodologies for navigating the complexities of financial markets, underscoring the significant potential of quantum approaches in the field of finance. These findings have theoretical implications for a variety of market stakeholders, offering strategic guidance and a reference point. We expect that the advancement of the quantum financial leapfrog theory will refine analytical methods and enhance investment strategies in practical financial applications.

Suggested Citation

  • Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:315-:d:1321676
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    References listed on IDEAS

    as
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