市场微观结构中的隐私补贴
The Privacy Subsidy in Market Microstructure
- The Open University of Japan（日本开放大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明做市商在粗化信号上定价必然产生隐私补贴，并刻画其在三个经典模型中的闭式形式，表明隐私在主导阶上福利中性且可内生化选择最优噪声规模。
AI中文摘要：
隐私保护的交易机制设计在对订单流的粗化视图上定价。我们证明，一个承诺在其结算的订单流的严格更粗的信号上进行信息有效（后验均值）定价的做市商，必然会将一个闭式福利转移让渡给交易者——即隐私补贴——并且，任何限于该粗信号的规则都无法同时满足针对已结算订单流的信息有效性和零利润。我们针对一般的粗化过程建立了这一不可能性，然后在三个经典微观结构模型中闭式刻画了该补贴：具有高斯流量噪声的单期Kyle模型、具有二元方向通道的Glosten-Milgrom模型，以及具有布朗通道的连续时间Kyle-Back模型。该补贴与损失对再平衡（Loss-Versus-Rebalancing）存在结构性对应关系，两者的福利率均分解为噪声驱动项的平方乘以承诺对象因子。在扣除费用前，该补贴是一种纯转移，可由盈亏平衡费用回收；一旦征收该费用，就会扭曲交易量，由此产生的无谓损失——在明确的交易配置价值下——相对于噪声规模为四阶，而总补贴为二阶，因此隐私在主导阶上对福利是中性的，且具有严格更小的不可回收损失。将隐私水平内生化，一个用差分隐私收益换取这种无谓损失的协议，会闭式地选择内点噪声规模；这样做保持了价格冲击与知情强度的半揭示乘积不变，同时将价格冲击的波动率弹性从其教科书值1上解锚定。
英文摘要：
Privacy-preserving exchange designs price on a coarsened view of order flow. We show that a market maker committed to informationally efficient (posterior-mean) pricing on a signal strictly coarser than the flow it settles necessarily cedes a closed-form welfare transfer to traders -- the privacy subsidy -- and that no rule restricted to the coarse signal is simultaneously efficient and zero-profit against the settled flow. We establish this impossibility for a general coarsening, then characterise the subsidy in closed form across three canonical microstructure models: single-period Kyle with Gaussian flow noise, Glosten-Milgrom with a binary direction channel, and continuous-time Kyle-Back with a Brownian channel. The subsidy obeys a structural correspondence with Loss-Versus-Rebalancing, both welfare rates factorising as a squared noise driver times a committed-object factor. Gross of fees the subsidy is a pure transfer recovered by a break-even fee; once levied, that fee distorts volume, and the resulting deadweight -- under an explicit allocative value of trade -- is fourth-order in the noise scale while the gross subsidy is second-order, so privacy is welfare-neutral to leading order with a strictly smaller irrecoverable loss. Endogenising the privacy level, a protocol trading a differential-privacy benefit against this deadweight chooses an interior noise scale in closed form; doing so leaves the half-revealing product of price impact and informed intensity intact while unpinning the volatility-elasticity of price impact from its textbook value of one.
