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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.06287 |
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| _version_ | 1866915548269379584 |
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| author | Xin, Tian |
| author_facet | Xin, Tian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum-Theoretical Re-interpretation of Pricing Theory Xin, Tian Pricing of Securities Quantum Physics 91G20, 60J35, 47D06, 35R09, 60J75, 60G51, 81S22, 91G80 G.3; G.1.10; I.6.5; J.4 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. |
| title | Quantum-Theoretical Re-interpretation of Pricing Theory |
| topic | Pricing of Securities Quantum Physics 91G20, 60J35, 47D06, 35R09, 60J75, 60G51, 81S22, 91G80 G.3; G.1.10; I.6.5; J.4 |
| url | https://arxiv.org/abs/2510.06287 |