We consider a model of a limit order book and determine the optimal tick size set by a social planner who maximizes the welfare of market participants. In a 2-period model where only two agents arrive sequentially, the tick size is a friction that constrains investors to use discrete price grids, and as a consequence the optimal tick size is equal to zero. However, in a model with sequential arrival of more than two investors who can endogenously either take liquidity or supply liquidity by undercutting or queuing behind existing orders, the tick size is positive: it is a strategic tool a social planner uses to optimally affect the choice made by investors between liquidity demand and supply. In addition, the optimal tick size is a function both of the value of the asset and of trading volume. The policy implication of such findings is that the European tick size regime and the “Intelligent Ticks” Nasdaq 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 empirical predictions.
Author(s): Giuliano Graziani, Barbara Rindi
Keywords: Limit Order Book, Tick Size, Social Planner, Undercutting, Queuing.