Jan Novotny | Searcharxiv

arXiv2026

Herding and Liquidity in Order-Book Markets. II. Fundamental Anchoring and the Resilience of Liquidity

An order-book market whose liquidity provision is anchored to a fundamental value carries a restoring force: the price mean-reverts to value and the book refills after a shock. We show this restoring force is a robust intrinsic stabiliser and identify it causally-dialling the anchor down removes the mean-reversion, and a leverage-driven fire-sale then self-sustains. Separately, we ask whether a stressed market transmits its liquidity stress to a coupled calmer one, and find that it cannot: across six transmission channels of increasing strength-cross-market herding, arbitrage flow, and market-maker withdrawal up to a funding-constrained population fire-sale and a leverage spiral-the receiver's stress is independent of whether its neighbour is stressed, at every anchor strength. Market-maker withdrawal thins the receiving book but does not ignite it. Our order parameter throughout is the one-sidedness of the book-liquidity stress rather than a directional price crash-so a liquidity crisis here means the sustained one-sidedness a failing anchor produces. A liquidity crisis in this model is a failure of fundamental anchoring, not of market making.

q-fin.TR↗

arXiv2026

Herding and Liquidity in Order-Book Markets. I. A Robust Liquidity-Stress Crossover and its Reflexive Mechanism

Agent-based models of markets readily produce emergent instabilities, but telling a genuine collective effect apart from a parameter artefact takes discipline. We apply Bouchaud's phase-diagram method to a continuous-double-auction order-book model. The method is to map the full phase diagram, test its robustness to rule changes, and rule out degenerate and numerical origins before we call any feature a tipping point. The model has fundamental-anchored zero-intelligence liquidity and a mid-anchored chartist herding layer, controlled by the fraction $\varphi$ and the strength $\kappa$ of herders. A 7x6 grid (336 runs, each with a scrambled-sign null) locates an emergent liquidity-stress crossover. The order parameter, the fraction of events with a one-sided book, rises to about 0.34 at $(\varphi,\kappa)=(0.9,1.0)$, is zero across all 42 scrambled cells, and forms a smooth crossover rather than a discontinuous Dark Corner. The dry-up is rule-robust (it recurs under an order-flow-imbalance rule), horizon-robust (about 0.32-0.35 across a 16x range of momentum window), and has a monotone onset boundary $\varphi^*(\kappa) = \{0.55, 0.45, 0.36\}$. We then decompose the mechanism at a matched directional-bias amplitude (mean |p_buy - 0.5| about 0.269). Price-momentum herding carries a large, comparator-robust reflexive component (+0.29; buying begets buying), whereas the order-flow rule's component is about 0 and comparator-dependent. The RMS-mispricing gradient is a placement artefact, largest at $\kappa=0$. A companion two-market analysis finds no directional cross-market contagion across a signal-only herding link.

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