Priority Ordering in Perpetual CLOBs: Measuring the Latency Tax on Takers

Abstract A taker facing a delayed view of a central limit order book does not merely receive an old price. The taker effectively grants faster counterparties a short-lived option: stale liquidity remains available when the market moves against its maker and disappears when it becomes favorable to the taker. This paper derives a minimal closed-form value for that asymmetry. If the efficient-price innovation over latency interval is Gaussian with volatility basis points per square-root second, the one-sided stale-quote cost is basis points per exposed fill. A seeded Monte Carlo with two million draws per latency point reproduces the formula within 0.16% across 10–500 ms. Under an illustrative—not estimated— bps/, model cost rises from 0.160 bps at 10 ms to 1.128 bps at 500 ms. The result supports the square-root scaling mechanism, not a claim about realized losses on any named venue. Public trade-level timestamps, quote-cancellation events, and queue positions are required to estimate an actual latency tax. Hypotheses H1 — Strong analytical support expected. Under a driftless diffusion and one-sided adverse selection, expected stale-quote optionality scales with rather than linearly with latency. H2 — Strong numerical support expected. A direct Monte Carlo should agree with the closed form to within 0.5% using two million independent paths per grid point. H3 — Exploratory and not identifiable from available observations. At realistic venue-specific volatility and cancellation behavior, the latency tax can equal or exceed a one-basis-point fee advantage. The model can identify break-even boundaries, but the staging data cannot establish where a production perpetual CLOB sits relative to them. Data Provenance This study deliberately separates measurements from assumptions. The primary analysis is SIMULATED with NumPy 2.x using fixed seed 20260710, two million independent Gaussian innovations at each of six latency points, and an illustrative volatility of 4 bps/. The data source for every simulated output is the included script and its saved JSON result. Closed-form values are mathematical derivations, not observations or confidence intervals. The daily staging snapshot was collected through Venym's operational databases and contained 944,150 funding-rate records, ten recent filled trades, and cross-exchange funding snapshots from Binance, Hyperliquid, and Asterdex. Those records provide market context only. They contain no synchronized order-book messages, cancellation acknowledgements, queue positions, or packet timestamps, so they are not used to estimate latency costs. The web research bundle supplied five contextual sources, including academic work on transaction ordering and general MEV references; none supplied a venue-level causal estimate suitable for reuse here. | Input or output | Provenance | Reliability | Appropriate interpretation | |---|---|---|---| | | Derived closed form | RELIABLE conditional on assumptions | Mechanism and scaling law | | Monte Carlo values | Seeded simulation, per point | RELIABLE as implementation check | Numerical validation only | | bps/ | Illustrative sensitivity parameter | UNRELIABLE for any venue | Scenario, not estimate | | Latency grid, 10–500 ms | Designed sensitivity grid | UNRELIABLE as market prevalence | Comparative scenarios | | Realized venue latency tax | Not observed | UNIDENTIFIABLE | Requires message-level data | | Funding and ten fills | Internal operational snapshot | RELIABLE as logged context; irrelevant to causal estimate | Motivation only | Mechanism: Latency Creates an Option Suppose the efficient midprice at the taker's decision time is . The taker sees or acts on a quote whose actionable state arrives after seconds. During that interval the efficient price changes by $\mathbb E[\max(Z,0)]=1/\sqrt{2\pi}q\in[0,1]q\sqrt{2}\taus\taufL(\tau)=1\sigma^\sqrt{s}\sqrt{s}\sqrt{s}\sqrt{s}qiM{i,t+\delta}\sqrt{s}q\sigma\sqrt{\tau/(2\pi)}$, making volatility and square-root latency the sufficient inputs. Two million seeded paths per latency point reproduce the formula within 0.16%, satisfying the numerical hypothesis. The paper's original contribution is a compact break-even framework linking latency to basis-point economics while keeping parameter reliability explicit. What this paper is: a reproducible pilot model and measurement blueprint. What it is not: evidence of realized extractable value on Hyperliquid or any other specific venue. The next step is not a more elaborate simulation; it is synchronized order-level data capable of estimating selective survival, queue loss, and post-fill markouts out of sample. References 1. Daian, P. et al. (2020). “Flash Boys 2.0: Frontrunning in Decentralized Exchanges, Miner Extractable Value, and Consensus Instability.” IEEE Symposium on Security and Privacy. 2. Adams, H. et al. (2024). “The Dark Side of the Mempool.” arXiv:2407.19572. Contextual source supplied by the research bundle. 3. Zhang, K. (2024). Research on bl