Currently, the situation is aggravating and the risks are increasing due to the fact that the bulk of transactions are now carried out by computers, working strictly according to algorithms, aimed mainly at achieving quick results without even minimal losses, and acting almost simultaneously, which can cause a chain collapse at stock exchanges uncoupled from the actual situation in the economy and the real value of assets. Meanwhile, the regulators do not have any meaningful and reliable tools for controlling and managing particularly explosive situations in financial markets, especially in organized markets or stock exchanges, where the prices of all global commodities and assets are largely determined. Such regulating agencies currently use accumulated historical experience and empirical parametric models to develop their management processes [Intriligator, 2002]. For these reasons, overcoming the apparent stagnation in the development of theoretical finance is a long overdue global task. The main challenge here and now is the almost complete absence of a mathematical apparatus with a potential to be used not only describe the exchange functioning as an asset pricing mechanism, which is done by financial econometrics at a qualitative level, but also accurately calculate the temporal fine price structure and the temporal fine structure of the trade volume during short time intervals, for example, during one trading session. Using the analogy with the scattering theory in physics, this can be formulated the other way around. Econometrics solves the so-called inverse problem, namely, extracting information about the studied system from the experimental data. The present study, however, aims at solving a direct problem – creating a fairly universal method for ab initio calculation of the exchange time microstructures with a characteristic size of a few seconds, which can be directly compared with the corresponding experimental fine structures of time trading dynamics, a method that could serve as a powerful tool for building a general theory of exchanges. We hope that the probabilistic theory of stock exchanges developed in this study can serve as a basis for building a general probabilistic financial theory and a deeper understanding of how the global world of finance works.