Insider Trading, Stochastic Liquidity and Equilibrium Prices

22 November 2013
Pierre Collin-Dufresne
We extend Kyle's (1985) model of insider trading to the case where liquidity provided by noise traders follows a general stochastic process. Even though the level of noise trading volatility is observable, in equilibrium, measured price impact is stochastic. If noise trading volatility is mean-reverting, then the equilibrium price follows a multivariate stochastic volatility `bridge' process. More private information is revealed when volatility is higher. This is because insiders choose to optimally wait to trade more aggressively when noise trading volatility is higher. In equilibrium, market makers anticipate this, and adjust prices accordingly. In time series, insiders trade more aggressively, when measured price impact is lower. Therefore, aggregate execution costs to uninformed traders can be higher when price impact is lower