发表机构
FRE department, Tandon School of Engineering, New York University（纽约大学坦登工程学院金融与风险管理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出广义朗之万模型刻画潜在流动性下的市场冲击，推导出中间平方根冲击区域，并证明冲击与波动率相关、与期限无关，且往返成本非负。
AI 中文摘要
我们将市场冲击建模为对提交订单流减去潜在交易者逆流的响应，当价格偏离无订单时本应达到的水平的位移超过个体阈值时，潜在交易者被激活。订单流消耗这一池子，而广义朗之万方程控制其在多个时间尺度上的恢复。其记忆核是指数函数的有限和，因此其马尔可夫提升是精确的而非近似。对于未耗尽的池子，在个体交易响应的显式假设下聚合，在线性小订单极限和大订单极限之间产生中间平方根区域，而无需强加平方根冲击定律。将阈值和响应随价格噪声缩放，使该区域中的冲击与波动率成正比，而随执行期限增长的阈值使其独立于持续时间。在恒定显示深度下，预期往返成本在对数价格约定下为非负，与记忆无关。数值实验表明，耗竭收窄了平方根范围，且产生相似单订单冲击的记忆谱在大量先前交易后可能做出不同响应。对市场数据的校准留给后续论文。
英文摘要
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.
Comments4 figures, 9 tables
