  We construct an equilibrium for the continuous time Kyle's model with
stochastic liquidity, a general distribution of the fundamental price, and
correlated stock and volatility dynamics. For distributions with positive
support, our equilibrium allows us to study the impact of the stochastic
volatility of noise trading on the volatility of the asset. In particular, when
the fundamental price is log-normally distributed, informed trading forces the
log-return up to maturity to be Gaussian for any choice of noise-trading
volatility even though the price process itself comes with stochastic
volatility. Surprisingly, we find that in equilibrium both Kyle's Lambda and
its inverse (the market depth) are submartingales.
