Kyle Model

The Kyle model (Albert Kyle, 1985) is a strategic model of informed trading in which a single risk-neutral insider with private information chooses how much to trade, knowing that a market maker will observe the total order flow and set prices to break even. Unlike the Glosten-Milgrom model, which treats informed traders as random arrivals, the Kyle model treats the insider as an optimizing agent who controls the rate of information release through trading.

The insider's problem is to maximize expected profit while minimizing the speed at which information is revealed. Trade too aggressively, and the market maker learns the private information immediately, collapsing the spread and eliminating profit. Trade too slowly, and the risk of the information becoming public before the position is complete erodes the advantage. The equilibrium is a linear strategy: the insider trades a constant fraction of the remaining information advantage in each period, producing a price path that follows a square-root law.

The Kyle model's deeper insight is that liquidity is endogenous to information structure. The market maker's pricing rule is not arbitrary; it is the optimal response to the insider's strategy. And the insider's strategy is not arbitrary; it is the optimal response to the pricing rule. The equilibrium is a fixed point in a game of incomplete information, and it shows that the very concept of 'market liquidity' is determined by the strategic interaction between informed and uninformed traders, not by the mechanical properties of the order book.

The model has been extended to multiple insiders, multiple trading rounds, and dynamic information, but its core message remains: the price process is not an exogenous random walk to which traders respond. It is an endogenous outcome of strategic behavior that the model itself determines.