Insider Trading, Stochastic Liquidity and Equilibrium Prices
Abstract
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