Strategic trading with information acquisition and long-memory stochastic liquidity

This paper investigates the strategic interaction of information acquisition, information-based dynamic trading, and noise trading patterns, as well as its significant implications on market equilibrium outcomes. We consider a market where the strategic trader can dynamically acquire costly information about an asset’s payoff via private signals instead of endowing him with its full information. The noise trading, which provides necessary liquidity for the market, has the feature of long-range dependence. The risk-neutral market maker then sets the equilibrium price for the asset based on information gleaned from the market total order flow. We characterize the equilibria for both opaque and transparent markets depending on whether or not the trader’s order flow is disclosed. In particular, closed-form solutions are obtained for two special cases and associated financial interpretations are provided. We find that: (1) the endogenous information acquisition and information-based trading help improve the price informativeness over time, while the information efficiency could be decreasing; (2) long-memory stochastic liquidity leads to an excessive price volatility; and (3) in a transparent market, the trader should adopt a mixed strategy by adding an additional noise term to the trading strategy to prevent rapid information leakage.