Abstract
Statistical property of price fluctuation plays an important role in the decision-making of financial investments. The traditional financial engineering uses the random walk hypothesis to determine derivative prices. However, it is well-known that the Black–Sholes–Merton formula to compute option prices tends to fail and one of the reasons for this failure has been attributed to the random walk hypothesis. Namely, the statistical distribution of actual price fluctuation does not necessarily follow the standard normal distribution but has a higher probability towards both tales than that of Gaussian. In other words, actual market prices are much riskier than the case predicted by the standard Gaussian random walk. Motivated by this fact, we investigated a large amount of data recently produced by the ultra-fast transaction of the Tokyo Stock Exchange (TSE) market at the level of sub-millisecond speed of transaction called as ‘Arrowhead’ stock market. After substantial numerical and statistical analysis of recent stock prices as well as index prices in TSE, we have reached a conclusion at a certain level of accuracy. Namely, non-Gaussian stable distribution corresponding to α < 2 is observed in various index data, while Gaussian distribution corresponding to α = 2 seems to be observed in the case of single stock price fluctuation at the limit of the sub-second time range. Those facts imply that the Gaussian assumption (α = 2) underneath the Black–Sholes formula cannot be used for the derivatives of index prices.
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Tanaka-Yamawaki, M., Yamanaka, M. (2020). Is the Statistical Property of the Arrowhead Price Fluctuation Time Dependent?. In: Czarnowski, I., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies. IDT 2020. Smart Innovation, Systems and Technologies, vol 193. Springer, Singapore. https://doi.org/10.1007/978-981-15-5925-9_41
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DOI: https://doi.org/10.1007/978-981-15-5925-9_41
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