Abstract
We study the statistical nature of stock price fluctuation in the ultrafast stock trading system called the “arrowhead market”. The first stage of this “arrowhead market” was started in the beginning of January 2010 at Tokyo Security Exchange market in order to reach the speed of transactions at the level of one millisecond. Then it was upgraded to the second stage to reach the speed of half a millisecond in September 2015, after the merge of Tokyo market and Osaka market to become Japan Exchange Group, Inc. Due to the immense size of the data, only one stock from October 2015 to December 2016 is treated in this article. The empirical distributions of stock prices converted to stock returns every 0.1 second follow the scaling law of the Lévy stable distribution of index α = 1.7 ± 0.3, as a result of scaling study of the coarse graining in the range of 0.8 seconds to 13 minutes. This result clarified that the distribution is consistent to the Lévy stable distribution, the same as our past study on the first stage of the arrowhead market, as a result of coarse graining in the range of 5 seconds to 2 minutes. Although preliminary, this result may imply that the efficient market is realized in the “arrowhead market”.
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