Essays on Trading and Contract Theory

This dissertation provides a study of optimal trading and contracting decisions, and their impacts on modern market structures. The dissertation is composed of three chapters.Chapter 1 investigates the impact of dark pools on the informational efficiency of prices (price discovery). Traders trade an asset in either an exchange or a dark pool, with informed traders having heterogeneous private signals whose distribution is determined by an information precision level. We find that dark pools have an amplification effect on price discovery. That is, when information precision is high, adding a dark pool enhances price discovery, whereas when information precision is low, adding a dark pool impairs price discovery. The main force behind this result is a sorting effect: in equilibrium, traders with strong signals trade in exchanges, traders with modest signals trade in dark pools, and traders with weak signals do not trade. These results produce novel empirical predictions regarding dark pools that reconcile the empirical evidence. The results also provide regulatory suggestions on enhancing the informational efficiency of pricing in equity markets and in emerging markets.Chapter 2 provides a framework to study information diffusion and interaction between a centralized and a bilateral market. In the model, traders trade to hedge their positions with some agents possessing private information. All agents can trade in the bilateral market before trading with a monopolistic market maker in a centralized market. We show that an active bilateral market functions as a channel to disseminate information. Moreover, information diffusion depends on the centralized market liquidity: both overly liquid and overly illiquid centralized markets discourage bilateral trading, and only reasonable centralized market liquidity activates bilateral trading and hence information diffusion. We also find that information diffusion is conducted in an asymmetric way. Which type of news spreads faster depends on the conjecture of the uninformed traders. Lastly, when prices in the centralized market contain information, it may ``squeeze out" trades and information diffusion in the bilateral market.Chapter 3, which is co-authored with Jen-wen Chang, analyzes the optimal screening decision for a monopolistic firm when consumers have time-inconsistent preferences and unobservable multiple degrees of naivet\'e (unawareness of their time-consistency). The firm can contract to screen their degrees of sophistication, subject to profit maximization. We characterize the optimal contracts and show that the firm offers a non-screening contract when consumers have deterministic costs and offers a screening contract when consumers have random costs. We argue that the uncertainty of the consumption costs lowers the firm's screening costs, and a discount per-usage price serves as a commitment device for the more sophisticated types. The results explain the phenomenon of the variation of contracts in sports club memberships, saving plans, and retirement programs