Contents I. Introduction
The price limits serving as a price stabilization mechanism have been widely used in futures markets since the global market crash of 1987. In a futures market with a daily price limit rule, trading is permitted only at prices within limits. Numerous studies have concentrated on examining the rationales or effectiveness of price limits, while a very limited number of researchers have tried to explore the design of appropriate price limits. Central to one line of these models is the minimizing objective function in which different costs caused by the imposition of price limits are taken into account. For example, Brennan (1986) assume that the total cost of participation in the market includes the opportunity cost of the margin requirement, the cost from the loss of liquidity due to the possibility of trading interruptions, and the cost of reneging[1]. Chou, Lin, and Yu (2000, 2003) extend the work of Brennan to investigate the spillover of unrealized residual shocks and the effectiveness of coordinating price limits across futures and spot markets[2],[3]. Another line of researches attempt to determine the optimal level of price limits capturing the trade-off between the costs and benefits. Acker and Hunter (1994) establish a descriptive model of optimal futures price limits. Costs include operating cost and illiquidity costs. Benefits include the prevention of excessive speculation, the provision of time to arrange for financing, and the limiting of overreactions to news [4]. Considering the impact of price limits in an asymmetric information framework, Anshuman and Subrahmanyam (1999) set an objective function with trade-off between the bid-ask spread and the quality of information to determine optimal price limits [5]. Though existing studies on price limits have contributed in different directions, they are a little far from practical use. First, the inquiry that what kinds of costs or benefits are caused by the imposition of price limits is not conclusive for the absence of a unified theoretical framework. Furthermore, such theoretical models in previous studies are difficult to be measured by historical trade data, that is, these models may fail to reflect the updated information in futures markets.
