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This is particularly valid in organized markets or exchanges where the prices of all global goods and assets are largely measured. All these management processes are currently reliant on tools using the analysis of accumulated historical experience and the use of empirical parametric models [Intriligator, 1971]. Therefore, overcoming the obvious stagnation in the development of theoretical finance is a long-overdue global task. The main challenge now is to overcome the near complete absence of a mathematical apparatus with which to describe the functioning of the exchange as an asset-pricing mechanism. Financial econometrics can do this qualitatively, but also required is the ability to calculate the temporal fine structure of the price and trade volume dynamics within short time intervals, such as during a single trading session.
Using a parallel with the physics theory of scattering, we can look at this differently. Econometrics focuses on solving the so-called «inverse problem», namely, the problem of extracting information from experimental data about the system under study. Conversely, we aim to solve a direct problem: the creation of a near-universal method of calculation from the first principles (ab initio) of the temporal exchange microstructures. These, with a characteristic time size of several temporal seconds, can be directly compared with the corresponding experimental fine structures of trading dynamics. This method could serve as a powerful tool for building a quantitative theory of exchanges.
We hope that in future, the probabilistic theory of exchanges developed in this study can serve as a basis for building a more general probabilistic financial theory. In doing so, a deeper understanding will be gained of how our global world of finance works.
It is obvious that organized markets are complex, multi-agent, non-equilibrium probabilistic systems, the description of which requires the application of adequate mathematical methods and apparatuses. The only suitable source of such methods and apparatuses is physics, where the experience of theoretical work with multiparticle systems with similar, formal structures has long been accumulated. In addition, quite a lot of experience has already been gathered in the application of the physical method in economics, namely, the use of formal methods and approaches of theoretical physics in solving economic problems.
In particular, probabilistic economic theory was developed [Kondratenko, 2005, 2015], a new theory of market economy. Initially, this theory was modeled on quantum mechanics with the derivation of economic equations of motion. Unfortunately, we are not yet able to accurately solve these equations for multi-agent markets. Because of this, a simpler version of the theory was later developed. It uses only the probabilistic method without solving equations of motion, namely, probability economics. It is used in this work as a basic theory for constructing probabilistic theory of exchanges. Although it contains no equations of motion, there is a mathematical apparatus that has proven very adequate and fruitful for describing exchange processes and structures.
To clarify, probability economics contains neither physics nor mechanics and, in particular, no quantum mechanics. This is an economic theory used to describe economic processes taking place on exchanges. This theory uses a mathematical apparatus which was created hundreds of years ago, and was previously used successfully to solve similar problems in physics. Probability economics has been developed in the spirit of both classical economic theory, and the physical method in economics. This variant has followed a figuratively similar evolutionary trajectory to the theories of Adam Smith to Karl Menger and onwards to Ludwig von Mises.
The works of these three authors have fostered my understanding of the essence and tasks of real economic science, as well as the desire to develop their ideas and concepts using the modern scientific probabilistic method of research. My primary task has been the creation of a mathematical apparatus adequate to the physical method and its use for the calculation of real economic systems. A similar process occurred during the creation and rapid rise of physical science, due to the creation of a powerful mathematical apparatus. It began with the discovery of the equations of motion and differential calculus.
The probabilistic method has long been applied at the empirical level in economic research by using the basic formulas of probability theory. The use of the probabilistic method in economics used an analogy with quantum mechanics of physical multiparticle systems [Kondratenko, 2005, 2015], and broadly pushed forward the framework of ideas and conceptions about the modern economic world. It gave rise to a new, probabilistic style of scientific economic thinking and created a new, dynamic probabilistic picture of the modern economic world. This veered away from the traditional static ideas of the economic mainstream, including neoclassical economic theory. This monograph solves the problem of this approach’s practical application to specific economic systems, or exchanges. There is enough input data in the form of supply and demand quotations for quantitative study, as well as enough relevant, experimental data in the form of market prices and trade volumes to verify the theory.
Probability economics is built in terms of probability distributions. These are usually accepted in various scientific fields; primarily in physics, in areas such as statistical and quantum physics. Emphasized here is that probability distributions create the basis and language of the probabilistic method used to study complex dynamical systems. The way in which real markets could be quantitatively described using methods of probability economics was demonstrated earlier [Kondratenko, 2005, 2015] using examples of small model commodity economies. Our work has succeeded in achieving the following goal: to create the foundation of the exchanges theory. Based on probability economics, it overcomes the disadvantages of the modern theory of finance described earlier, and results are in good agreement with the respective experimental exchange data.
The microscopic theory developed in this work is devoted to the study of various exchange structures and processes at the level of exchange agents, and more precisely, at the level of actions of individual exchange agents. By this we mean the mechanisms of formation of exchange microstructures, such as temporal price and trade volume fine structure which depending on the quotations of market agents at each particular time. This theory gives a microscopic view of exchanges and exchange phenomena.
Our book will show how probability economics gives a reasonably accurate, microscopic description of the exchange phenomena. Regularities and patterns are derived from the detailed structures and mechanisms of work, found in the formation of prices and trade volumes.
We emphasize that for the purposes of this study there is no difference between stock, commodity and other exchanges. The theory being developed is equally suitable for describing any exchange, so henceforth we will use the term “stock exchanges”, or simply “exchanges”. As the main example for the study, several days of intraday dynamics occurring between 2013 and 2020 were chosen of Sberbank shares, Brent crude oil futures («Brent futures») and US dollars on the Moscow Exchange (MOEX) in Moscow.
The quotations of exchange agents used in this case are available on the MOEX website for a small fee, so all the numerical results of this work and its conclusions can be easily verified by other researchers. In addition, the intraday dynamics of Brent futures for several days of 2020 on the Intercontinental Exchange Futures Europe (ICE) in London were similarly studied.