Shmuel Baruch

Who Benefits from an Open Limit‐Order Book?*

The NYSE opened the limit-order book to off-exchange traders during trading hours. We address the welfare implications of this change in market structure. We model a market similar to the auction that the exchange uses to open the trading day. We consider two different environments. In the first, only the specialist sees the limit-order book, while in the second the information in the book is available to all traders. We compare equilibria and find that traders who demand liquidity are better off when the book is open while liquidity suppliers are better off when the book is closed.

Insider trading and risk aversion

Abstract This paper is a continuous time version of Holden and Subrahmanyam (Economics Letters 44 (1994) 181). The paper extends Kyle (Econometrica 53 (1985) 1315) by introducing risk aversion on the side of the monopolist informed trader and allows for the liquidity traders instantaneous demand to depend on cost of trading, as well as on the risk of the stock. The main result of the paper is that, in equilibrium, the price pressure decreases with time regardless of the elasticity of the liquidity demand function.

Strategic Liquidity Provision in Limit Order Markets

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.

Informed Trading and Price Discovery before Corporate Events

Stock prices incorporate less news before negative events than positive events. Further, informed agents use less price aggressive (limit) orders before negative events and more price aggressive (market) orders before positive events (buy–sell asymmetry). Motivated by these patterns, we model the execution risk that informed agents impose on each other and relate the asymmetry to costly short selling. When investor base is narrow, security borrowing is difficult, or the magnitude of the event is small, buy–sell asymmetry is pronounced and price discovery before negative events is lower. Overall, we show that the strategies of informed traders influence the process of price formation in financial markets, as predicted by theory.

Inferior Goods, Giffen Goods, and Shochu

According to a well-known result by W. Hildenbrand [6], if all consumers possess the same demand function and the density of the expenditure distribution is decreasing, than the average income effect term is non-negative even if inferior goods are present, so that the aggregate demand must be monotone. We show that if the expenditure density is uni-modal and a certain relation between the income density and individual demand is satisfied, than the average income effect term is negative and Giffen goods are not ruled out. We show that the lowest-grade rice-based Japanese spirit (shochu) satisfies this condition. The data suggest that this commodity might be a Giffen good.