A Finite Bid--Ask Spread from Replenishment Displaced from the Quote
Abstract
We give a unified analytic account of a finite bid--ask spread in a two-field reaction--diffusion order book. The model retains separate bid and ask densities in operational time, with diffusion, cancellation, reaction and external order creation. On the symmetric equal-coefficient branch, the imbalance field determines the reaction price, while the total standing density carries the spread geometry. A market-making source is introduced by withholding order placement over a finite interval around the reaction boundary, representing round-trip replenishment displaced from the quote. Under a separated, quasistationary and weak-overlap approximation, transport penetrates inward from the placement edges over the cancellation length, giving the quoted spread as the sub-threshold core of the placement-source-free interval. Market orders remove standing density at the observed quote, whereas replenishment is delivered outside it and must diffuse back across the penetration depth. We derive the resulting delayed and attenuated quote-level response in operational time. On that branch, finite spread and price impact arise from distinct response sectors, while their calendar-time appearance requires a separate observation clock.
Related
- Is Earthquake Replenishment Sufficient for Unbiased b-Value Estimation?
- Random Order in Quantum Streaming: Replenishment and Robust Lower Bounds
- Earth-scale searches for displaced vertices: KM3NeT meets the LHC
- Displaced e+e- Signatures from an X17-Mediated Inelastic Dark-Sector Cascade
- Vertexing displaced diphoton decays with recoil photons at Belle II
BibTeX
@misc{angstmann2026finite,
title = {{A Finite Bid--Ask Spread from Replenishment Displaced from the Quote}},
author = {Christopher Angstmann and Derick Diana and Tim Gebbie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07985},
eprint = {2610.07985},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07985},
}
RIS
TY - UNPB
TI - A Finite Bid--Ask Spread from Replenishment Displaced from the Quote
AU - Christopher Angstmann
AU - Derick Diana
AU - Tim Gebbie
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.07985
UR - https://arxiv.org/abs/2610.07985
AB - We give a unified analytic account of a finite bid--ask spread in a two-field reaction--diffusion order book. The model retains separate bid and ask densities in operational time, with diffusion, cancellation, reaction and external order creation. On the symmetric equal-coefficient branch, the imbalance field determines the reaction price, while the total standing density carries the spread geometry. A market-making source is introduced by withholding order placement over a finite interval around the reaction boundary, representing round-trip replenishment displaced from the quote. Under a separated, quasistationary and weak-overlap approximation, transport penetrates inward from the placement edges over the cancellation length, giving the quoted spread as the sub-threshold core of the placement-source-free interval. Market orders remove standing density at the observed quote, whereas replenishment is delivered outside it and must diffuse back across the penetration depth. We derive the resulting delayed and attenuated quote-level response in operational time. On that branch, finite spread and price impact arise from distinct response sectors, while their calendar-time appearance requires a separate observation clock.
ER -