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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

Chinese

我们在两个领域的反应 - 散布命令书中提供一个有限的报价 - 请求扩散的统一分析账户。该模型在运行时间内保持单独的报价和请求密度,通过散布,取消,反应和外部命令创建。在对称的平等系数分支上,不平衡场决定了反应价格,而总站着密度携带了扩散几何。通过在反应边界周围的有限间隔内保持订单放置,代表了从报价中移动的轮回补充。在一个分开的、四分位和弱覆盖的接近下,运输从取消长度的放置边缘穿透到放置边缘,使报价作为放置源 - 无报价订单的次要核心扩散。市场要求在报价密度

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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