Regularities in stock markets

From the stock markets of six countries with high GDP, we study the stock indices, S&P 500 (NYSE, USA), SSE Composite (SSE, China), Nikkei (TSE, Japan), DAX (FSE, Germany), FTSE 100 (LSE, Britain) and NIFTY (NSE, India). The daily mean growth of the stock values is exponential. The daily price fluctuations about the mean growth are Gaussian, but with a nonzero asymptotic convergence. The growth of the monthly average of stock values is statistically self-similar to their daily growth. The monthly fluctuations of the price follow a Wiener process, with a decline of the volatility. The mean growth of the daily volume of trade is exponential. These observations are globally applicable and underline regularities across global stock markets.