Do price limits hurt the market?

Actually, our model is a variant of the TASM. It is written in C\(++\) on the Borland C\(++\) Builder 6, and is built from the perspective of object-oriented programming (OOP). In addition, the DA mechanism is employed to determine market prices, while a simple price adjustment scheme which is purely based on the excess demand is considered in the previous version of the TASM.

The value of \(K\) can be set as 1, 12, 52, and 250 when the trading periods are a year, month, week, and day, respectively.

Unlike Arthur et al. (1997) and LeBaron et al. (1999), traders in our model are not presumed to have any idea about the stock’s fundamental value. Directly deriving \(E_{i,t}(\cdot )\) by the GP may lead the price dynamics quite volatile. Therefore, we confine the expectations formation to an appropriate range that may be perceived as some sort of prior knowledge.

With this kind of functional form, the traders are still able to take a chance on the martingale hypothesis when \(f_{i,t}=0\). A similar functional form with the same motif is also employed in Chen and Yeh (2001).

Our software code is currently provided on the web: http://​comp-int.​mis.​yzu.​edu.​tw/​faculty/​yeh/​software/​.​ The interested readers can freely download and test it.

In Anufriev and Panchenko (2009), market dynamics under different market mechanisms such as Walrasian auction, price- and order-driven trading protocols are examined. Pellizzari and Westerhoff (2009) investigate the effects of a transaction tax under a continuous double auction market and a dealership market.

The amount of \(\varDelta h\) is selected under the consideration of market size, i.e. the number of traders in the market. Of course, the quantities of each transaction may play an important role. In practice, each trader should also independently make a decision regarding how many shares of stock he would like to trade. Incorporating this factor into the trader’s decision may involve a new development that makes the modeling of traders’ behavior quite complicated. In addition, the results obtained in such a framework would be biased if the number of traders in our simulations were not so large, e.g. 100 in our simulations. However, the simulations with large market size, e.g. 500 or above, are quite time consuming. Due to the constraint on our current computational resources, it would not be practical for us to perform such large-scale simulations to examine this issue at the moment.

During the 1972–2008 period, the \(\alpha \) values of the Dow Jones Industrial Average Index (DJIA), Nasdaq Composite Index, and the S&P 500 are 3.74, 3.71, and 4.02, respectively.

During the 1972–2008 period, the Hurst exponents of the raw returns (absolute returns) of the DJIA, Nasdaq, and the S&P 500 are 0.53, 0.56, and 0.53 (0.96, 0.97, and 0.96), respectively.

In actual fact, we have examined the markets with larger price limits, such as 20 and 30 % price limits. We find that, even though the frequency of (locked) limit hits is quite low, traders’ heterogeneity, e.g. the standard deviations of reservation prices and expectations, is not the same as that in the market without price limits.

The results regarding volatility and price distortion have been presented and compared with those of Westerhoff (2003) in Yeh and Yang (2010).

Of course, there are other patterns for the relationship between \([P^{R, L}, P^{R, U}]\) and \([P^{L}, P^{U}]\). However, according to our simulation results, approximately 99 % of all locked limit days belong to the case of \([P^{L}, P^{U}]\subset [P^{R, L}, P^{R, U}]\).

The ranges here are selected under the consideration that our market is not large enough. Excessively large ranges will make some traders significantly dominate the market dynamics. The purpose of maintaining the total shares of stock being 100 is to keep the fundamental value invariant.

Actually, we also conduct the simulations where traders’ initial shares of stock are uniformly distributed over [0, 5] with the constraint on the total shares of stock being 100, and initial amount of money is uniformly distributed over [100, 1000]. Most of the properties regarding the tests of the three hypotheses do not change.