In an extension of the Kyle (1985) model of continuous insider trading, it is shown that asymmetric information can make it impossible to price options by arbitrage. Even when an option would appear to be redundant, its introduction into the market can cause the volatility of the underlying asset to become stochastic. This eliminates the potential for dynamically replicating the option. The change in the price process of the asset reflects a change in the information transmitted by volume and prices when the option is traded.

In an extension of the Kyle (1985) model of continuous insider trading, it is shown that asymmetric information can make it impossible to price options by arbitrage. Even when an option would appear to be redundant, its introduction into the market can cause the volatility of the underlying asset to become stochastic. This eliminates the potential for dynamically replicating the option. The change in the price process of the asset reflects a change in the information transmitted by volume and prices when the option is traded.

The continuous-time version of Kyle’s (1985) model of asset pricing with asymmetric information is studied. It is shown that there is a unique equilibrium pricing rule within a certain class. This pricing rule is obtained in closed form for general distributions of the asset value. A particular example is a lognormal distribution, for which the equilibrium price process is a geometric Brownian motion. General trading strategies are allowed. In equilibrium, the informed agent, who is risk neutral, has many optima, but he does not correlate his trades locally with the noise trades nor does he submit discrete orders.

In a Kyle (1985) model, the sign of the correlation between a firm's debt and equity returns is the same as the sign of the cross-market Kyle's lambda. The sign is positive (negative) if private information concerns the mean (risk) of the firm's assets. We show empirically that information conveyed by order flows is primarily about asset means. The cross-market lambdas are quite large; consequently, the portions of bond and stock returns explained by order flows are highly correlated, even though the order flows themselves are virtually uncorrelated.

The investment boundaries defined by Grenadier (2002) for an oligopoly investment game determine equilibria in open-loop strategies. As closed-loop strategies, they are not equilibria, because any firm by investing sooner can preempt the investments of other firms and expropriate the growth options. The perfectly competitive outcome is produced by closed-loop strategies that are mutually best responses. In this equilibrium, the option to delay investment has zero value, and the simple NPV rule is followed by all firms. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]., Oxford University Press.

We characterize and prove the existence of Nash equilibrium in a limit order market with a finite number of risk-neutral liquidity providers. We show that if there is sufficient adverse selection, then pointwise optimization (maximizing in p for each q) in a certain nonlinear pricing game produces a Nash equilibrium in the limit order market. The need for a sufficient degree of adverse selection does not vanish as the number of liquidity providers increases. Our formulation of the nonlinear pricing game encompasses various specifications of informed and liquidity trading, including the case in which nature chooses whether the market-order trader is informed or a liquidity trader. We solve for an equilibrium analytically in various examples and also present examples in which the first-order condition for pointwise optimization does not define an equilibrium, because the amount of adverse selection is insufficient.

This paper analyzes models of securities markets with a single strategic informed trader and competitive market makers. In one version, uninformed trades arrive as a Brownian motion and market makers see only the order imbalance, as in Kyle (1985). In the other version, uninformed trades arrive as a Poisson process and market makers see individual trades. This is similar to the Glosten–Milgrom (1985) model, except that we allow the informed trader to optimize his times of trading. We show there is an equilibrium in the Glosten–Milgrom-type model in which the informed trader plays a mixed strategy (a point process with stochastic intensity). In this equilibrium, informed and uninformed trades arrive probabilistically, as Glosten and Milgrom assume. We study a sequence of such markets in which uninformed trades become smaller and arrive more frequently, approximating a Brownian motion. We show that the equilibria of the Glosten–Milgrom model converge to the equilibrium of the Kyle model.

We compare a sealed-bid uniform-price auction (the Treasury’s experimental format) with a sealed-bid discriminatory auction (the Treasury’s format heretofore), assuming the good is perfectly divisible. We show that the auction theory that prompted the experiment, which assumes single-unit demands, does not adequately describe the bidding game for Treasury securities. Collusive strategies are self-enforcing in uniform-price divisible-good auctions. In these equilibria, the seller’s expected revenue is lower than in equilibria of discriminatory auctions.

We analyze competition among informed traders in the continuous‐time Kyle(1985) model, as Foster and Viswanathan (1996) do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam (1992) that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity.