Reflective model of the stock market

Abstract

The paper presents a new conceptual approach to analyzing processes in the stock market. The elementary mathematical model of the market is based on the mutually agreed dynamic description of the queue of buyers and sellers and the main actual parameters of the market — the price and executed volumes of transactions. The principal feature of the model is the description of the participants of supply and demand based on two parametric gamma distributions. The parameters of the distribution are the integral behavioral characteristics of bidders, called conditionally — "fear" and "greed". It is shown that the values of fear and greed, formalized with the help of gamma distribution, can be estimated quantitatively. A reflexive mechanism of transactions is proposed to display the interaction of bidders. This mechanism has two-way feedback. Current values of fear and greed of buyers and sellers determine the price change and the volume of transactions. In turn, price changes and fulfilled volumes lead to changes in fear and greed for supply and demand. The results of numerical simulation of the simplest market fluctuation caused by external influence are presented. Two main stages of this process are considered: 1) external influence leads the market from the state of initial equilibrium to the excited non-equilibrium state, 2) after the end of the influence, the market returns to equilibrium at a new price level. It is suggested that the proposed method can be used not only to describe the securities market, but also for other financial markets, as well as for modeling various social interactions.