SUMMARYWe built an artificial market model and investigated the impact of large erroneous orders on financial market price formations. Comparing the case of consented large erroneous orders in the short term with that of continuous small erroneous orders in the long term, if amounts of orders are the same, we found that the orders induced almost the same price fall range. We also analysed effects of price variation limits for erroneous orders and found that price variation limits that employ a limitation term shorter than the time erroneous orders exist effectively prevent large price fluctuations. We also investigated effects of up-tick rules, adopting the trigger method that the Japan Financial Services Agency adopted in November 2013.We also investigated whether dark pools that never provide any order books stabilize markets or not using the model including one lit market, which provides all order books to investors, and one dark pool. We found that markets become more stable as the dark pool is increasingly used. We also found that using the dark pool more reduces the market impacts. However, if other investors' usage rates of dark pools become too large, investors must use the dark pool more than other investors to avoid market impacts. When a tick size of a lit market is larger, dark pools are more useful to avoid market impacts. These results suggest that dark pools stabilize markets when the usage rate is under some threshold and negatively affect the market when the usage rate is over that threshold. Our simulation results suggest the threshold might be much larger than the usage rate in present real financial markets.This study is the first to discuss whether or not several concrete and actually adoptable regulations, including those that have never been employed (e.g. price variation limits with various parameters), could prevent large fluctuations of market prices, including those beyond our experience, using artificial market simulations, and to discuss quantitatively how spreading of dark pools beyond our experience could affect market price formations using the artificial market simulations. In short, this study is the first study to comprehensively discuss how regulations and financial systems beyond our experience could affect price formations using the artificial market simulations.

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Keywords: efficiency of stock market, dark pool, market maker, high frequency trading, multi agent-based simulation SummaryIn recent financial market, high frequency traders (HFTs) and dark pools have been increasing their share. Financial analysts have speculated that they might decrease market transparency and malfunction price discovery, and their interaction would make the situation worse.To validate speculations, artificial market simulation is a tool of study by constructing virtual markets on computers. In this research, by constructing an artificial market simulation, we analyzed how the interaction between HFTs and a dark pool impacts on the market efficiency (in the sense of price discovery) of a (lit) stock market. In simulations, two types of trader agents enter the market. A market maker agent, a representative strategy of HFTs, submit orders to the lit market. We analyzed the market maker's interest rate spread, or simply the spread, as a key parameter for their strategy. Stylized trader agents submit orders to either the lit market or the dark pool with some probability given as a parameter.The simulation results suggest that on the condition that market makers have little impact to market pricing (having a large spread), moderate use of dark pools can promote market pricing. On the other hand, on the condition that market makers have big impact to market pricing, excessive use of dark pools can inhibit market pricing, while using dark pools do not have bad influence when the rate of use is not high. On the influence of market makers, our results suggest that the bigger the impact to market pricing (a small spread), the more it can promote market pricing.