Mathematical modeling of integral assessments of the exchange rate in foreign exchange dealing
The development of information technology in financial markets has led to the emergence of Internet Trading and gave birth to a new actively developing type of business in Russia - dealing services. Dealing refers to short-term operations of banks and other financial institutions to manage their assets on the world Foreign Exchange Market.
When applied to the financial market, the concept of "dealing" can be interpreted as the actions of a dealer - a natural or legal person engaged in "buying and selling" financial instruments (securities, foreign currencies, commodity or financial contracts or any other derivative financial instruments) at his own expense for the purpose of making a profit. DealerAs a rule, a dealer must be a member of an exchange (stock, currency or commodity exchange) where the corresponding "purchase and sale" operations are made. Any financial instruments, with the help of which a dealer makes profit, can be bought by him for the basic settlement currency, which in the world financial market is the US dollar (since 1974 it is the world reserve currency).
Modern real economic systems have a high level of uncertainty due to the complexity of internal relationships and the impact of a large number of factors, the impact of which is not always possible to foresee and take into account. At the same time, systems can change randomly, with a change in the structure of the elements, which determines a new state of the system, qualitatively different from the previous ones. This generates unstable and unsteady development of all its processes. These problems do not allow to describe processes in detail using traditional approaches, in particular - mathematical description in the form of systems of differential equations. Therefore, to solve the problems foreign exchange dealing methods based on the methods of neural network theory and dynamic programming technology, automatic control theory, probability theory and mathematical statistics, singular decomposition apparatus, as well as methods of forecasting motion of nonstationary processes in complex real systems should be used. Besides, there is a necessity of applying a systematic approach to solving the problems of forecasting nonstationary processes in complex systems, in particular the processes taking place on financial markets. The property of non-stationarity in complex systems manifests itself in two aspects: in the emergence of trends, characterized by fundamental dependencies in the system; and in the appearance of some jumps, the sources of which are random in time events and shocks of individual factors. Figure 1 shows an example of one of the main macroeconomic processes, The data is based on the data of the exchange rate of EUR/USD, which characterizes the changes in the exchange rate of EUR/USD. On the vertical axis the value of the closing price change in points is plotted; on the horizontal axis - time, the data was obtained with the help of MetaTrader terminal.
Fig. 1. Changes in the EUR/USD exchange rate on the monthly and weekly interval.
It is possible to describe the process (see Fig. 1) as an object consisting of elementary components corresponding to different sources, characterized by groups of movements defined by trend, harmonic and random components. This description of the process structure focuses the study on revealing the integrity of the internal mechanisms of functioning, revealing the diverse types of connections of the complex object. In this case, the simplicity of elements is limited by the presence of properties of the system itself and the availability of information on its characteristics. This circumstance allows to increase efficiency of forecasting, because the allocated components of movement have predictable character and simpler mathematical description, which schematically can be represented in the form of sum the simplest trend componentscorresponding to the main factors of motion of a complex system; the sum of elementary harmonic components of motion, determined by a set of various periodic factors; and the random component, formed by a set of various random factors. Based on certain features of the system approach, one of the requirements for methods is their ability to decompose the object under study into separate structural components and the possibility of reverse synthesis by separate elements of the resulting structure to solve the prediction problem.
In view of the above, it is necessary to consider the methodology of mathematical modeling of integral evaluations exchange rateThe modeling is a creative process, and it is very difficult to put it into a formal framework. Modeling is a creative process and it is very difficult to put it into a formal framework. Let us consider the main stages of modeling, which in its most general form can be represented step by step in the following way:
Each time when solving a specific task, such a scheme may be subjected to some changes: some block may be removed or improved. All stages are determined by the task and the goals of the simulation.