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Impact of maker-taker fees on stock exchange competition from an agent-based simulation

Abstract

One fee structure offered by stock exchanges is maker-taker fees, in which the exchange pays rebates to traders who place limit orders and collects trading fees from traders who place market orders. A stock market that employs maker-taker fees is thought to outpace its stock market competition in the sense that its relative market volume share will increase due to the expectation of efficient market formation. However, whether this idea is true has not been sufficiently investigated. Therefore, in the present study, we constructed two artificial markets, one with maker-taker fees and the other without them, and investigated how the trading shares of these two markets vary. We also calculated and compared market liquidity, volatility, and efficiency of the two markets. As a result, the market volume share of the market with maker-taker fees was found to increase with the rebate amount when the stock exchange provided sufficient rebates. Otherwise, the market with maker-taker fees lost market volume share to the market without maker-taker fees. In addition, we found that market liquidity increased and volatility decreased in the market that adopted maker-taker fees. In the market that does not adopt maker-taker fees, market liquidity and volatility did not necessarily improve. In contrast, market efficiency was found to improve in both markets.

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Notes

  1. A limit order is a buy order or sell order that is placed at a specific price.

  2. A market order is a buy order or sell order that is placed without specifying a price.

  3. Bid means buy, and ask means sell. The best bid quote is the highest buy order price and the best ask quote is the lowest sell order price.

  4. In this study, we use logarithmic returns. Therefore, the expected return is the difference between the logarithm of the current price and the logarithm of the expected price, that is, \({r_e}^t_j=\ln {{P_e}^t_j}-\ln {P^{t}}=\ln {({P_e}^t_j/P^{t})}\), which allows us to derive Eq. (3).

  5. The reason why \(t_e=1{,}000{,}000\) was chosen is that this value was sufficient to grasp the trend of the experiment, and no difference in the trend occurred even if the period was extended.

  6. Varying parameters such as the profit expected by the exchange (\(R_{EX}\) in the model) may change the boundary between intervals A and B, but the tendency for the share to change similarly depending on the amount of rebate is not expected to change.

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Appendices

Appendix

A Validity of artificial market models

Many empirical studies have pointed out that in real markets, statistical properties such as fat tails and volatility clustering (stylized facts) appear [6, 22]. A fat tail is a condition in which a frequency distribution (histogram) is created from data on the rate of change of prices, and the kurtosis is large and the bottom of the distribution is thicker compared to a normal distribution. When the kurtosis is positive, the distribution has a fat tail. Volatility clustering refers to the tendency for large changes in returns to be followed by large changes for some time, and small changes to be followed by small changes [15]. This is quantitatively indicated by the fact that returns and autocorrelations of squared and absolute values of returns are positive even when there is a lag.

In this model, the parameters were set to reproduce stylized facts and to keep the model as stable as possible. To achieve these goals, we followed the model of Yagi et al. [24]. As an example, Table 2 shows the stylized facts when the basic maker-taker fees are not adopted and \(R_\mathrm{M}\)=– 0.050%. The lag used in 2 indicates the degree of shift in the autocorrelation of the squared returns. Label lag1 indicates the autocorrelation between the t-period and the \(t-1\)-period, and label lag2 indicates the autocorrelation between the t-period and the \(t-2\)-period. As can be seen from this table, both the kurtosis and the autocorrelations are positive.

Table 2 Stylized facts (with \(R_\mathrm{M}\)=-0.050%)

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Hoshino, M., Mizuta, T., Sudo, Y. et al. Impact of maker-taker fees on stock exchange competition from an agent-based simulation. J Comput Soc Sc (2022). https://doi.org/10.1007/s42001-022-00169-5

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Keywords

  • Maker-taker fees
  • Share of trading volume
  • Stock exchange competition
  • Multi-agent system
  • Agent-based simulation