We generalize the seminal framework of Kyle (1985) to a many-asset setting, bridging the gap between informed-trading theory and modern trading practices. Specifically, we formulate an infinite-dimensional Bayesian trading game in which the informed trader's private information may concern arbitrary aspects of the cross-sectional payoff structure across a continuum of traded assets. In this general setting, we obtain a parsimonious equilibrium characterized by a single scalar fixed point, yielding closed-form characterizations of equilibrium trading strategy, price impact within and across markets, and the informational efficiency of equilibrium prices.

In a noisy environment, dynamic contracts allow a principal to implement any noiseless, one-shot, incentive-compatible outcome from a risk-neutral agent's actions. That is, the principal may eventually observe the agent's hidden type and hidden history of actions. Thus, dynamic contracts improve upon the static second-best when the principal's payoff is concave in output (e.g., due to risk aversion or payoff concavity in signal).

In noisy environments with adverse selection and moral hazard, dynamic contracts can induce a risk-neutral agent's actions to deterministically implement any one-shot, incentive-compatible outcome. Thus, dynamic contracts improve upon the static second-best when the principal's payoff is concave in output, e.g., due to risk aversion or payoff concavity. We bring out a new intuition that applies to both principal-agent and limited commitment settings (such as Kyle, 1985)-in both settings, the informed agent can be induced to reveal all his private information.

We consider price discovery across derivative markets in a general framework where an agent has private information regarding state probabilities and trades state-contingent claims. In an equivalent options formulation, the informed agent has private information regarding arbitrary aspects of an underlying asset's payoff distribution and trades option portfolios. We characterize the informed demand, price impact, and information efficiency of prices. The informed demand formula prescribes option strategies for trading on any given aspect of the underlying payoff, thereby rationalizing and extending those used in practice for trading on, e.g., volatility.

The role of algorithmic traders as arbitrageurs and their impact on price efficiency in the foreign exchange market are examined. Algorithmic traders do not improve price efficiency by detecting and exploiting mispriced currency pairs. On the contrary, algorithmic traders contribute to the creation of possible arbitrage opportunities as a byproduct of intensified competition among liquidity providers. On the other hand, the same market-making competition also prevents the creation of arbitrage opportunities via tightening of spread. Moreover, the leftover inventory problem impedes the implementation of round-trip arbitrage trades - thereby rendering many "arbitrage opportunities" that do appear spurious. The latter two factors explain the reduced occurrence of arbitrage opportunities under the increased algorithmic trading presence observed in data.

We study price discovery in a model where an informed agent has arbitrary private information about state probabilities and trades state-contingent claims. The model unifies the seminal frameworks of Arrow and Debreu (1954) and Kyle (1985). When the claims are options, the informed agent has arbitrary information about the underlying asset's payoff distribution and trades option portfolios. We characterize the informed demand and cross-market information dynamics. Our results provide the first equilibrium-based explanation for longstanding empirical practices and regularities in option markets, such as common trading strategies and the volatility smile across option strikes.

We obtain an invariance principle for the two-dimensional Brownian sheet where the underlying random field need not be independent or stationary. We demonstrate the application of this result towards spatial unit root tests in a basic setting.

We formulate a measure of information efficiency in a general, no-arbitrage semimartingale model of the price process. The market quality measure is applied to a high-frequency dataset from the interdealer FX market to identify changes in market efficiency after a decimalization of tick size.

Existing research has documented that tighter regulation tends to restrain banking activity.Nevertheless, the extent to which this effect depends on global financial conditions is relatively unknown. This paper identifies two theoretical mechanisms that relate the regulatory arbitrage behavior of internationally active banks (IABs) to global financial conditions. According to the first mechanism, regulation becomes more binding during adverse global financial conditions and IABs face higher compliance costs in more regulated markets. According to the second mechanism, regulation suppresses the degree of risk-taking so that highly-regulated countries are more insulated from global financial risk. Using the BIS international banking statistics and a unique empirical strategy, we find that the first mechanism is more prevalent. IABs expand their claims on less-regulated countries more rapidly when global financial conditions are tight. However, the relationship goes in the opposite direction under loose global financial conditions. Structural vector autoregressive estimations at the country level provide supporting evidence.

We consider an extension of the Kyle (1985) model where Arrow-Debreu securities are traded and the informed trader has private information regarding arbitrary higher moments of the asset payoff distribution. In this setting, we analyze price discovery and informed demand of Arrow-Debreu securities---equivalently, options. The informed trader strategy in our model is consistent with options trading strategies used to trade on higher moments in practice. The probability law of market maker's posterior is independent of specification of asset payoffs. The information efficiency of Arrow-Debreu prices decreases with respect to the dispersion of the informed trader's private signal.

This paper identifies two theoretical mechanisms that relate the regulatory arbitrage behavior of internationally active banks (IABs) to global financial conditions. According to the first mechanism, regulation becomes more binding during adverse financial conditions. Under these conditions, IABs face higher compliance costs in more regulated markets. According to the second mechanism, higher regulation suppresses the degree of risk-taking and asset returns so that highly-regulated nations are more insulated from global financial risk. These results are reversed in less-regulated nations. We use a panel of bilateral BIS banking statistics and a unique empirical strategy to find that the first of the two theoretical mechanisms above is more prevalent. Specifically, IABs expand their claims more rapidly in less-regulated nations when global perception of financial risk is higher. The direction of arbitrage is reversed under loose conditions. This evidence is corroborated by the inferences from a structural vector autoregressive model fitted to data from individual countries.

The limiting distribution of the normalized Fourier coefficients of a spatial autoregressive process obeying a model having dependent errors is investigated. Normalizing factors of the Fourier coefficients of both the moving average and autoregressive error structure models are found.

We consider a time series regression with a time-varying parameter and long-range dependent data. No restriction is placed on the behavior of the time-varying parameter, allowing for both smooth changes and abrupt breaks.The time-varying parameter is estimated by a nonlinear orthogonal series estimator which is shown to have mini max estimation error and no spurious jumps in the large sample limit.

We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel data models.

This paper develops a model of the optimal timing of interest rate changes. With fixed adjustment costs and ongoing uncertainty, changing the interest rate involves the exercise of an option. Optimal policy therefore has a “wait-and-see” component, which can be quantified using option pricing techniques. We show that increased uncertainty makes the central bank more reluctant to change its target interest rate, and argue that this helps explain recent observed deviations from the Taylor Rule. An optimal wait-and-see policy fits the target interest rates of the Fed and Bank of Canada better than the Taylor Rule.

We obtain an invariance principle for two-dimensional Brownian sheet where the underlying random field need not be independent or stationary. The invariance principle is applied to obtain and analyze a frequency-domain test for spatial unit root against local-to-unity alternatives.

We consider the problem of testing for unit root in time series where the error term of the series is near unit root. As the error term approaches unit root, existing tests no longer retain reasonable small sample properties. We introduce a test statistic that is well-behaved in small sample under such condition. Empirical applications reject the unit root null hypothesis for macroeconomic series, such as unemployment and consumer prices, where conventional unit root tests have been unable to do so.

We tested the viability of partnering with local developers to create custom annotation applications and to recruit and motivate crowd contributors from their communities to perform an annotation task consisting of the assignment of toxicity ratings to Wikipedia comments. We discuss the background of the project, the design of the community-driven approach, the developers' execution of their applications and crowdsourcing programs, and the quantity, quality, and cost of judgments, in comparison with previous approaches. The community-driven approach resulted in local developers successfully creating four unique tools and collecting labeled data of sufficiently high quantity and quality. The creative approaches to the rating task presentation and crowdsourcing program design drew upon developers' local knowledge of their own social networks, who also reported interest in the underlying problem that the data collection addresses. We consider the lessons that may be drawn from this project for implementing future iterations of the community-driven approach.

Jason Baldridge, Tania Bedrax-Weiss, Daphne Luong, Srini Narayanan, Bo Pang, Fernando Pereira, Radu Soricut, Michael Tseng, Yuan Zhang. Proceedings of the First International Workshop on Spatial Language Understanding. 2018.