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A Finite Bid--Ask Spread from Replenishment Displaced from the Quote

Christopher N. Angstmann, Derick Diana, Tim Gebbie · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.07985 · cited by 0 works (OpenAlex) · open-access PDF

Korean

우리는 두 필드 반응 - 배포 명령서에서 유한 bid-ask 확산에 대한 통합 분석 계정을 제공합니다. 모델은 배포, 취소, 반응 및 외부 순서 생성과 함께 작동 시간에 별도의 bid-and-kind 밀도를 유지합니다. 시메트리 균형 요소 부서에서 불균형 필드는 반응 가격을 결정하며 총 서있는 밀도는 확산 기하학을 수반합니다. 시장 형성 소스는 반응 경계 주변의 유한한 간격에 걸쳐 배포 명령을 유지함으로써 도입됩니다. 분리 된, 쿼시스타리 및 약한 접근 접근 접근으로 반응 가격을 결정합니다. 전송은 취소 길이를 넘어서 배포 한 위치에서 배포 한 위치를 취소 한 위치에서 배포 한 위치를 배포함으로써

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Finite set, Order (exchange), Core (optical fiber), Interval (graph theory), Mathematics, Mechanics

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