Вероятностная теория фондовых бирж

Анатолий Васильевич Кондратенко, 2021

В данной монографии излагаются основы вероятностной теории фондовых бирж, построенной на базе вероятностной экономической теории. Аналитические и численные методы данной теории использованы для расчетов временной динамики рыночных цен и объемов торгов различными активами на Московской Бирже и Intercontinental Exchange Futures Europe в течение одной торговой сессии и детального сравнения результатов расчетов с экспериментальными данными. Это сравнение демонстрирует хорошее согласие теории и эксперимента, которое позволяет утверждать, что в монографии была решена основная научная задача данного исследования – показано, что вероятностная экономическая теория находит экспериментальное подтверждение и тем самым обретает твердое экспериментальное обоснование. Для специалистов в сфере финансов, эконофизики и физической экономики, а также для профессиональных инвесторов и биржевых трейдеров.

Preface

This monograph is the third book in the series [Kondratenko, 2005, 2015, 2021] that develops probabilistic economic theory. When the first book was being prepared for publication sixteen years ago, I was asked when I thought this theory would gain wide acceptance from economists. My answer was: «No sooner than twenty years from now». To simply offer an alternative economic theory was not enough; I needed to show how it was better, and to prove that it is correct and capable of making reliable forecasts of economic development.

This monograph demonstrates the theory’s validity, and precisely the way in which it is better than other theories. Its effectiveness is shown when applied to important, organized markets such as stock exchanges. Based on the obtained results, a method is proposed for forecasting economic dynamics. Below, I will explain why stock exchanges were chosen as the objects of research.

It is well known that the division of labor by the various producers of goods improved the well-being of humankind during the early stages of civilization. This led to the subsequent formation and development of capitalism across the world. Initially, this process was dominated by ordinary markets, which facilitated and thereby accelerated the process of goods and services exchange between people. Eventually, this evolved to occur between organized markets, the more complex of which we have today such as the commodity, financial, and currency markets, amongst others. Together, their existence forms the exchange economy.

Currently, this exchange economy has, and effectively uses, all the most modern means of e-commerce, including artificial intelligence and algorithmic computer trading. Fueled by the widespread use of the Internet, the exchange economy is lightning fast, virtual and truly global. It is the high speed of information exchange and number of transactions that distinguishes the new virtual exchange economy from the traditional real economy. However, this feature of exchange trading can generate additional risks, both for the exchange economy and for the real economy. To date, these risks are only superficially understood in the economic academic community.

In today’s global economic world, the role of exchanges has become so significant that it is no exaggeration to say that the entire global economy is increasingly evolving towards an exchange economy. It would be more appropriately referred to as the transformation of the global economy into a financial economy, but in this monograph we will focus only on the role of exchanges in the economy. Therefore, we will use the term «exchange economy».

In today’s economy, the main purpose of exchanges is to determine prices for all tradable assets, including various types of money (currencies). Exchanges also facilitate trading and finance global economic activity. However, it is important to note that the state of affairs of all exchanges are good indicators of the entire global economic situation. The paradox of this status in the global exchange world is that there is clearly no adequate status in the world of theoretical finance. An adequate theory of organized financial markets still does not exist, which means there is no adequate theory representing the global real economy. This situation generates certain risks of the emergence and uncontrolled development of negative trends in the financial markets. This can lead to large-scale financial and, in turn, global economic crises, which we regularly observe in real life.

The generator of almost all economic crises in modern history are financial crises, the trigger of which are exchange crashes. Currently, the situation is exacerbated and the risks are increasing. This is because the bulk of transactions are now made by computers. Working strictly according to algorithms aimed mainly at achieving quick results, they guarantee the absence of even minimal losses. They act almost synchronously, which can cause a chain reaction of collapse on the exchanges in isolation from the real state of affairs in the economy, and from the real value of assets. Meanwhile, regulators have no meaningful or reliable tools to monitor or manage any particularly volatile situations in the financial markets.

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.

The book is written in the form of a research report, as it presents the results of practical application of the original economic theory. This was developed earlier by the author, specifically to quantitatively solve the direct problem for the exchange markets that were described earlier. As far as we know, there are no other documented studies of this type. For this reason, the book does not provide a detailed overview of the history of the issue, and references are made only to works whose results were used in the development of this theory. Moreover, hundreds of books and articles on econophysics and physical economics have been published relatively recently [Mantegna et al., 1999; Chernavsky D. et al., 2002; Farmer et al., 2005; Richmond et al., 2013; Ippoliti and Cheng (eds.), 2017], as well as articles by David Orrell, for example [(Orrell, 2020]. Together, the latter can be seen as an excellent modern overview of the application of theoretical physics methods used to describe economic phenomena.

Bear in mind that when basing a new economic model that resembles of one from physics, it is useful to employ the latter during the initial stage to help name and define new concepts. We have done so in this book by establishing parallels between the economic many-agent systems, and many-particle systems from physics. This applies, for example, to such terms as microscopic and macroscopic theories, direct and inverse problems, equations of motion, etc. Time will tell which of these new concepts and terms will take root in economics.

In conclusion, we summarize the monograph with a subjective assessment of the results obtained and the conclusions of the study. This monograph presents the basics of the probabilistic theory of exchanges, based on probabilistic economic theory using agent quotations provided by exchanges. By its nature, this exchange theory is microscopic, so its analytical and numerical methods make it possible to calculate and describe various exchange microstructures and microprocesses.

Calculations of this kind, first performed in this study, are also published for the first time in this monograph. Particular attention has been paid to the calculation of market prices and trade volumes of various assets (Sberbank shares, futures for Brent crude oil, US dollars) on the MOEX and ICE (Brent crude oil futures) during one trading session, along with a detailed comparison of the theoretical results with the corresponding experimental data. This comparison demonstrates a good agreement between the theory and experiment, which allows us to assert that the main scientific problem of this study is solved in the monograph. We demonstrate that probabilistic economic theory finds its experimental confirmation and thereby acquires a solid experimental justification. This radically distinguishes it from several other economic theories that have a heuristic or empirical character.

Another important task is also solved here, namely, the economic mechanism underlying the formation of market prices and trade volumes. This is described in detail and serves as a bridge connecting the microscopic economic world with the macroscopic economic world. The formation process of the macrocosm from the microcosm is hereby demonstrated. We show how the action and time dynamics of the exchange market as a whole are formed from the actions of exchange agents. A new, universal system of stock indices of assets, exchanges and the global system of exchanges has also been developed.

Similarly, a strategy has been developed for digitalization, forecasting and management of a country’s and the world’s economy. This is based on digital platforms used to accumulate the plans of economic agents, processing them using the formulas of probabilistic economic theory. If implemented, these will in turn improve the quality of public economic administration of the country, and the world.

This study demonstrates the importance and significance of stock exchanges as experimental economic laboratories, aimed primarily at testing models, evaluating model parameters and, ultimately, verifying existing and new economic theories. If we look at probabilistic economic theory, it was predominantly developed using the business world as an experimental laboratory, where the significant business experience of the author was formalized applying mathematical apparatus from theoretical physics. In the present study, using MOEX and ICE as experimental laboratories, probabilistic theory of stock exchanges has been developed by the author.

Our work consistently reveals great prospects in the further use of exchanges as powerful modern experimental economic laboratories. Some 300-500 years ago theoretical physics arose from the science of the solar system, and similarly, modern economic science will arise from the development of exchanges theory. It will consist of a closely interacting probabilistic economic theory and experimental stock exchange economics. Meeting all the generally accepted standards of the natural sciences, it will remain a humanitarian and social science.

Acknowledgments

Participants of the project «Quantum Finance Investments» of Investment Company EXCELLENCE Vitaly Martynovich and Maria Makarkina made a great contribution to the success of the project. The computer platform «QUANTUM FINANCE» was developed mainly by Vitaly Martynovich and Maria Makarkina, which they implemented in the C# language. This was used to perform calculations of exchange structures by applying the methods of probabilistic economic theory. Maria Makarkina also provided significant assistance in the preparation of this monograph for publication. I sincerely thank them both for their fruitful, long-term cooperation.

I respond with gratitude to Dmitry Sviridenko, who took on the important responsibility as executive editor of the monograph.

Thanks also go to the reviewers of the monograph Sergey Parinov and Yuri Perevyshin for the difficult work done at a highly professional level in reviewing the manuscript that presented the new theory.

I am grateful to the Alexander von Humboldt Foundation (Alexander von Humboldt Stiftung), which, many years ago, provided a scholarship that allowed him to see firsthand in West Germany how developed market economies work and how financial markets function within them.

I am grateful to the Moscow Exchange and the Intercontinental Exchange Futures Europe, which provided us with access to historical data and online quotations.

I also express gratitude to the Investment Companies FINAM and Interactive Brokers for the excellent implementation of the intermediary broker functions with the MOEX and ICE exchanges, respectively.

I sincerely thank the first reader of the manuscript of the book Konstantin Gluschenko for valuable comments and recommendations. Taking them into account made the material of the book more understandable for readers who adhere to orthodox economic views.

In conclusion, after a very long delay, I would like to pay off some my old debts. Firstly, to express gratitude to Vladimir Evstigneev for the informal, but very informative and useful review of my first book on the topic of probabilistic economic theory [Kondratenko, 2005]. Ksenia Kondratenko also deserves a big thank you for her help in preparing the manuscript of this book. Secondly, I note the important role played in this study by the professor of California University (Berkeley) George Judge, who applauded and supported enthusiastically that book many years ago, for which I am immensely grateful to him.

Anatoly V. Kondratenko Russia, Novosibirsk, September 2021

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