Fluctuation Distributions and Dynamics of Indexed Markets

Market price distributions and price fluctuation distributions have developed an increasing research and investment interest since about a century ago, as such distributions have usually been featured by displaying a peak profile with fat tails. In this work we consider a recent model that has successfully explained such fluctuation distribution profiles to currencies and commodities, by considering prices as temporally confined around a mean price, that jump to subsequent prices according to market activity. Thus, this model considers market prices hopping in time from supply-demand equilibrium points according to market forces. We consider such model to better understand the dynamics of indexes from a wide diversity of trading floors. Here, the hopping model successfully depicts fluctuation distributions at relatively short times, i.e., when intraday prices are considered. The inherent dynamics to indexes belong to diffusion as the mean squared price displacement displays a linear time relation to almost all studied indexes. Therefore, our study correctly differentiates fast and slowly diffusing indexes, indicating which markets exhibit faster or slower dynamics. Moreover, we find a particular index, the FTSE50, hallmarked by dynamics faster than diffusion. Here, the fluctuation distribution hopping model stops being efficient in depicting price fluctuation at a time where super diffusion is observed. Nevertheless, establishing an order in index dynamics, from fast to slow diffusion, allows considering the efficiency of different markets as diffusion should be observed at weak markets in terms of efficiency and the Efficient Market Hypothesis. The efficiency of each floor can be ordered, and even it can be considered that to stock floors as the ones considered, semi strong or strong efficiency is not reached, thus market agents are not able to reach all market information in time.