  In this paper, the Kyle model of insider trading is extended by
characterizing the trading volume with long memory and allowing the noise
trading volatility to follow a general stochastic process. Under this newly
revised model, the equilibrium conditions are determined, with which the
optimal insider trading strategy, price impact and price volatility are
obtained explicitly. The volatility of the price volatility appears excessive,
which is a result of the fact that a more aggressive trading strategy is chosen
by the insider when uninformed volume is higher. The optimal trading strategy
turns out to possess the property of long memory, and the price impact is also
affected by the fractional noise.
