Liquidity and the Marginal Value of Information
We revisit the Kyle (1985) model of price formation in the presence of private information. We begin by using Back's (1992) approach, demonstratingthat if standard assumptions are imposed, the model has a unique equilibrium solution, and that the insider's trading strategy has a martingale property. That in turn implies that the insider's strategies are linear in total order flow. We also show that for arbitrary prior distributions, the insider's trading strategy is uniquely determined by a Doob h-transform that expresses the insider's informational advantage. This allows us to reformulate the model so that Kyle's liquidity parameter is characterized by a Lagrange multiplier that is the marginal value or shadow price of information. Based on these findings, we can then interpret liquidity as the marginal value of information.