Moment approach to the descriptin of dynamic of stock price

Orlov Evgeniy
Candidate of Physical and Mathematical Sciences, Assistant Professor, Odessa National Economic University. E-mail:orlov_ev@onu.edu.ua

Cite this article:

Orlov E., (2018) Moment approach to the descriptin of dynamic of stock price. Ed.: М.D. Baldzhy (ed.-in-ch.) and others [Systema pensiinoho zabezpechennia Ukrainy ta yevrointehratsiini protsesy; za red.: М. D. Baldzhy (gol. red.)], Scientific Bulletin of the Odessa National Economic University (ISSN 2313-4569), Odessa National Economics University, Odessa, No. 10(262), pp. 161-177.

Abstract

To describe the dynamics of stock prices, diffusion models are used, which allow to take into account the random nature of price behavior depending on time. Such an approach does not take into account the discontinuous nature of the stock price behavior and therefore does not allow modeling behavior in all time intervals. In this case, price jumps are modeled by the Poisson process, which, together with the diffusion component, allows us to describe the behavior of the dynamic system. But this problem can be considered on the other hand, namely, with the help of ideas about the behavior of dynamic systems. A dynamic system can be in two equilibrium states in which there is no energy dissipation. In both of these states, the system is non-dissipative. However, if we consider the transition from one equilibrium state to another, then the energy dissipates. Therefore, in general, the system becomes dissipative. Examples of such systems can be observed in various fields of science: in physics, chemistry, biology and economics. In particular, the typical behavior can be observed depending on the price of stocks on time. In this work on the basis of the method of moments, modeling of the dynamic characteristics of dissipative systems, such as stock prices, has been carried out. Taking into account only even moments does not allow describing the presence in the system of forces that are dissipative in nature. Therefore, when building the characteristics of the system, odd moments were also taken into account. This made it possible to obtain the correct behavior of the diffusion coefficient of the considered system. Since the dependence under consideration is of a stochastic nature, to verify the adequacy of the proposed model, it is necessary to coordinate the behavior of its dynamic characteristics. In particular, the diffusion coefficient, viscosity, sedimentation, scattering and others. The results of the work allow us to further build computer models of the considered economic process.

Keywords

stock price dynamics, moment approach, dissipative systems, non dissipative systems, nonequilibrium processes, stock price jumps.

JEL classification: G120

UD classification: 336.018

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