The application of statistical methodologies and probabilistic results of power laws (PLs) could prove useful for financial modelling and risk quantification. In this project, we delve into the connections between financial markets, PLs, extreme value theory (EVT), and stochastic processes such as α-stable processes. We provide empirical applications of statistical methods based on PLs and EVT results using real high-frequency data for stock indexes in the Japanese (Nikkei 225) and United Kingdom (FTSE 100) markets, where we reproduce statistical analyses from the references but also discuss interesting patterns found and their implications for financial practice. Moreover, we discuss the relevance of different probabilistic forces, distributions, and processes found in the econophysics literature and the different methodologies considered to estimate relevant elements for our analysis.