Non-Stationary vs. Stationary Equilibrium  in  Dynamic Limit Order Markets

We solve non-stationary and stationary models of a limit-order market to investigate time dynamics and the effects of adverse selection and path dependency on equilibrium strategies, market quality, welfare, and price discovery. These effects depend on volatility.  With high volatility, informed-investors act as speculators, and increased adverse selection improves market quality and the welfare of uninformed-investors who become the best liquidity providers. With low volatility, the informed act as market makers and crowd out the uninformed, and increased adverse selection reduces uninformed welfare despite improving market quality. Our analysis delivers new results on liquidity, order informativeness, welfare, and transmission mechanisms.

Optimal Tick Size

We use a model of a  limit order book to determine the optimal tick size set by a social planner who  maximizes the welfare of market participants. Our results show that when investors arrive sequentially and supply liquidity by undercutting or queuing behind existing orders, the optimal tick size is a positive function of the asset value and a negative function of the stock liquidity. Intuitively, the tick size is a strategic tool a social planner uses to optimally affect investors' choice between liquidity demand and supply, thus mitigating the inefficiencies created by excessive undercutting and queuing.  The policy implication of such findings is that both the European tick size regime  and the 2022 SEC proposal dominate Reg. NMS Rule 612 that formalizes the tick size regime for the U.S. markets. Using data from the U.S. and the European markets we test our model's predictions.

Trading @ the Close 

In light of the growing concern of regulators about the substantial increase in closing auction volumes around the world, we find no evidence that increases in auction activity in Europe harm market quality during continuous trading. These results differ from findings in the US markets where a different type of closing auction mechanism is used.