On the quantum hydrodynamical reformulation of the Black–Scholes model

In this short paper, we present a quantum hydrodynamical reformulation of the Black–Scholes equation via a Wick rotation and the Madelung transformation. In this framework, the system’s self-organizing dynamics are governed by a quantum potential that is directly related to the normalized Greeks Delta and Gamma measures in option pricing. We examine classical limits and the sensitivity of this potential to volatility and the risk-free interest rate, and outline how the formulation supports quantum-hardware implementations of option-pricing dynamics.