Quantum-Theoretical Re-interpretation of Pricing Theory

• URL: http://arxiv.org/abs/2510.06287v2
• Date: Mon, 13 Oct 2025 07:24:54 GMT
• Title: Quantum-Theoretical Re-interpretation of Pricing Theory
• Authors: Tian Xin,
• Abstract summary: Motivated by Heisenberg's observable-only stance, we replace latent "information" with observable transitions between price states.<n>On a discrete price lattice with a Hilbert-space representation, shift operators and the spectral calculus of the price define observable frequency operators and a translation-invariant convolution generator.<n>Noncommutativity emerges from the observable shift algebra rather than being postulated.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by Heisenberg's observable-only stance, we replace latent "information" (filtrations, hidden diffusions, state variables) with observable transitions between price states. On a discrete price lattice with a Hilbert-space representation, shift operators and the spectral calculus of the price define observable frequency operators and a translation-invariant convolution generator. Combined with jump operators that encode transition intensities, this yields a completely positive, translation-covariant Lindblad semigroup. Under the risk-neutral condition the framework leads to a nonlocal pricing equation that is diagonal in Fourier space; in the small-mesh diffusive limit its generator converges to the classical Black-Scholes-Merton operator. We do not propose another parametric model. We propose a foundation for model construction that is observable, first-principles, and mathematically natural. Noncommutativity emerges from the observable shift algebra rather than being postulated. The jump-intensity ledger determines tail behavior and short-maturity smiles and implies testable links between extreme-event probabilities and implied-volatility wings. Future directions: (i) multi-asset systems on higher-dimensional lattices with vector shifts and block kernels; (ii) state- or flow-dependent kernels as "financial interactions" leading to nonlinear master equations while preserving linear risk-neutral pricing; (iii) empirical tests of the predicted scaling relations between jump intensities and market extremes.

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