潜在流动性、记忆效应与凹形市场冲击
文章 arXiv papers · 作者: Andrey Itkin
总结
该模型通过提交的订单流和潜在交易者的抵消性活动解释市场冲击。当价格超出各自阈值时，这些交易者便会入场，而订单流会消耗他们可提供的流动性。广义 Langevin 方程描述多个时间尺度上的恢复过程；由于其记忆核是指数函数之和，该模型可以精确表示为马尔可夫系统。
在所述交易者反应假设下，未耗竭的流动性池会对极小和极大的订单产生线性冲击，而不同交易反应的聚合会形成中间的平方根区间。模型还将该区间内的冲击与波动率联系起来，并在阈值缩放假设下使其与执行时长无关。数值实验发现，流动性耗竭会缩小平方根区间；孤立订单冲击相近的流动性记忆谱，在大量先前交易后可能表现不同。市场数据校准被留给配套论文，因此本文描述提供的是理论和数值证据，而非实证校准。
核心观点
- 价格越过各自的触发阈值后，潜在交易者会提供反向订单流。
- 订单流会消耗潜在流动性，模型描述其在多个时间尺度上的恢复过程。
- 交易反应聚合后可产生中间的平方根冲击区间，无须直接假设该定律。
- 在指定假设下，模型推导出波动率缩放和与执行时长无关的结果。
- 流动性耗竭会缩小平方根区间，市场数据校准留待后续研究。
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全文
# A Generalized Langevin Model of Latent Liquidity and Concave Price Impact # A Generalized Langevin Model of Latent Liquidity and Concave Price Impact We model market impact as the response to submitted order flow net of counterflow from latent traders, activated when price displacements from the level that would prevail without the order exceed individual thresholds. Order flow depletes this pool, and a generalized Langevin equation governs its recovery over several time scales. Its memory kernels are finite sums of exponentials, so its Markovian lift is exact rather than an approximation. For an undepleted pool, aggregation under explicit assumptions on individual trading responses yields an intermediate square-root regime between linear small- and large-order limits, without imposing a square-root impact law. Scaling thresholds and responses with price noise makes impact in this regime proportional to volatility, and thresholds that grow with the execution horizon make it independent of duration. With constant displayed depth, expected round-trip costs are nonnegative under the log-price convention, independently of the memory. Numerical experiments show that depletion narrows the square-root range and that memory spectra producing similar single-order impacts can respond differently after substantial prior trading. Calibration to market data is left to a companion paper.
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