Asymptotic Glosten Milgrom equilibrium

This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback type. Therefore a weak formulation of equilibrium is proposed. In this weak formulation, the inconspicuous trade theorem still holds, but the optimality for the insider's strategy is not enforced. However, the insider can employ some feedback strategy whose associated expected profit is close to the optimal value, when the order size is small. Moreover this discrepancy converges to zero when the order size diminishes. The existence of such a weak equilibrium is established, in which the insider's strategy converges to the Kyle optimal strategy when the order size goes to zero

Price, Trade Size, and Information Revelation in Multi-Period Securities Markets

We study price formation in securities markets, using the sequential trade framework of Glosten and Milgrom. This paper makes one basic methodological advance over previous research on sequential securities trading: we allow for multiple trade sizes for traders to choose from in a multi-period market. We examine how trade size multiplicity affects the intertemporal dynamics of trading strategies, bid-ask spreads, and information revelation. We also show that price impact, as a function of trade size, is increasing and exhibits (discrete) concavity.

Herd behavior and contagion in financial markets

We study a sequential trading financial market where there are gains from trade, that is, where informed traders have heterogeneous private values. We show that an informational cascade (i.e., a complete blockage of information) arises and prices fail to aggregate information dispersed among traders. During an informational cascade, all traders with the same preferences choose the same action, following the market (herding) or going against it (contrarianism). We also study financial contagion by extending our model to a two-asset economy. We show that informational cascades in one market can be generated by informational spillovers from the other. Such spillovers have pathological consequences, generating long-lasting misalignments between prices and fundamentals

How markets slowly digest changes in supply and demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.Comment: 111 pages, 24 figure

Information thermodynamics of financial markets: the Glosten-Milgrom model

The Glosten-Milgrom model describes a single asset market, where informed traders interact with a market maker, in the presence of noise traders. We derive an analogy between this financial model and a Szil\'ard information engine by {\em i)} showing that the optimal work extraction protocol in the latter coincides with the pricing strategy of the market maker in the former and {\em ii)} defining a market analogue of the physical temperature from the analysis of the distribution of market orders. Then we show that the expected gain of informed traders is bounded above by the product of this market temperature with the amount of information that informed traders have, in exact analogy with the corresponding formula for the maximal expected amount of work that can be extracted from a cycle of the information engine. This suggests that recent ideas from information thermodynamics may shed light on financial markets, and lead to generalised inequalities, in the spirit of the extended second law of thermodynamics

Price effects of trading and components of the bid-ask spread on the Paris Bource

Time Series;Prices;Financial Markets;Supply and Demand

Generalized second law of thermodynamics in the Glosten-Milgrom model

We derive an upper bound for the expected gain of informed traders in the Glosten-Milgrom model with finite horizon, fully analogous to a generalized second law of thermodynamics. This result extends that obtained by Touzo et al. a couple of years ago. The proof relies on Bayesian inference (exploiting the invariance of the problem under consecutive game sequences) and an interesting entropic inequality. We also provide numerical results both supporting the existence of a characteristic timescale in the model and illustrating the magnitude of gain fluctuations. Other possible extensions are discussed.Comment: 13 pages, 6 figure