خصوصیات بازار ارز با استفاده از مدل آستانه معامله گر

We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, autocorrelation of price change and non-Poissonian intervals. We also clarify the causality between microscopic dealers’ dynamics and macroscopic market's empirical laws.

Mathematical models of open markets can be categorized into two types. In one type, the market price time series are directly modeled by formulation such as a random walk model, ARCH and GARCH models [1] and [2], and the potential model [3], [4] and [5]. The other type is the agent-based model which creates an artificial market by computer programs [6], [7], [8] and [9]. The agent-based model is able to clarify the relationship between dealers’ actions and market price properties. Just like the simple ideal gas model reproducing basic properties of real gas, we can expect that simple dealers’ actions can reproduce the empirical laws of market prices. In this paper we systematically introduce four deterministic dealer models in order to clarify the minimal actions of dealers to satisfy the empirical laws of markets. These are revised models of so-called the threshold model which is originally introduced by one of the authors (H.T.) and coworkers [9] in order to demonstrate that dealers’ simple actions can cause deterministic chaos resulting the market price apparently random even the dealers’ actions are completely deterministic. We revise the model step-by-step to reproduce most of the empirical laws.

We started with the model-1, the basic dealer model. Considering why the model-1 differs from real market data, we added two effects to the model-1, both are feedback effects. One is the “self-modulation” introduced in the model-2, and the other is the “trend-follow” applied in the model-3. The model-4, applying both of these effects, satisfies most of the basic empirical laws. It should be noted that each dealer has only three parameters describing his character. Finally, we summarize our results in Table 1. Table 1. Results of each model Model-1 Model-2 Model-3 Model-4 Correlation of price change – – – S Distribution of volatility – – S S Distribution of intervals – S – S Diffusion of price – – – S –: Not satisfy; S: satisfy. Table options Sato and Takayasu already showed that the dealer model's price fluctuations can be approximated by ARCH model in some conditions [13]. Such approach of connecting the stochastic description of market models to dealer-based artificial market models will be fruitful study in the near future.