When large trades are not news: Liquidity tail risk and price discovery
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摘要
This paper develops a dynamic competitive limit-order-book model in which uninformed liquidity demand exhibits heavy tails (Student-t with ν > 2). The key insight is that the tail risk of liquidity demand acts as a state variable that modulates how informative large trades are about fundamental value. When liquidity shocks are light-tailed, very large orders strongly signal private information, but with heavy-tailed liquidity demand, the same large imbalances can reflect rare liquidity shocks, leading to flatter and more concave price impact and slower learning. The authors establish a fixed-point characterization of the equilibrium on a tail-controlled compact class, prove existence of such fixed points, analyze Bayesian learning of the fundamental value, and derive tail asymptotics for price impact that depend on ν, the number of informed traders, and the posterior beliefs. They also provide numerical solutions showing nonlinear, concave margins, persistence of adverse-selection premia, and power-law scaling in large-order regions, consistent with the analytical results. This work identifies liquidity tail risk as a structural variable shaping price discovery, spreads, and market impact [page::0][page::2].
