پویایی درونی بازارهای مالی: تعامل و اطلاع رسانی

We investigate the process that different interactions between investors will prompt information to propagate along a differentiated path and construct a financial market model. As information spreads, increasingly investors are attracted to participate in trading, then the “herding effect” is magnified gradually, which will induce the topology of market network to change and the price to fluctuate. Especially, under different initial conditions or parameters, the peak and fat-tail property is produced and the obtained statistic values coincide with empirical results: the power-law exponents between the peak value of return probability distribution and the time scales range from 0.579 to 0.747, and the exponents between the accumulation distribution and the return on the tail are close to 3. Besides, the extent of volatility clustering in our produced price series is close to that of S&P 500 and locates between NASDAQ and HSI. All the results obtained here indicate that the continuous variation of the “herding effect” resulting from information propagation among interacting investors may be the origin of stylized facts of price fluctuations.

In recent years, masses of financial data can be obtained more easily, many methods in statistical physics have been applied to the study on financial markets, and lots of stylized facts in financial markets have been accepted, such as peak-fat-tail non-normal behavior [1], [2], [3], [4], [5], [6] and [7], long range correlation [8] and [9], volatility clustering [10] and [11] and so on [12], [13], [14], [15] and [16]. Obviously, such stylized facts don’t match the framework of rational exception and homogeny assumption. Then a new method is needed to give the corresponding explanation. Because an agent-based model could describe an agent’s heterogeneity and bound ration more easily, lots of finance agent-models [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27] and [28] have been built to search the underlying market mechanism. Almost all agent-based financial models are composed of two parts, one is trade rules, also called price determination in some literature, and the other is mechanism design. For the former, there are three types of rules to determine the price. The first [17], [18], [19] and [20] is that price evolves with the imbalance between supply and demand, as in Eq. (1) equation(1) pt=f(pt−1,D(t)−S(t))pt=f(pt−1,D(t)−S(t)) Turn MathJax on where D(t)D(t) and S(t)S(t) denote the demand and supply at time tt respectively. The second [21], [22], [23], [24] and [29] describes such a process: there is a true order book where agents post their offers to buy or sell shares, then the equilibrium price is decided to promote the trade volume to be maximized. The third [25] and [26] is that clearing price will be given by market makers at every step. For the latter, there are two types of mechanism design. The first focuses on the detailed description of agents’ behaviors [19], [20], [21], [22], [29] and [25]. Generally agents learn from their past performances or from their neighbors, then inductively adapt their strategies. The second follows with interest in the heterogeneous interactions among agents and information dissemination [17], [18], [27], [28], [30], [31], [32] and [33]. To investigate information transmission and communication among agents, the percolation model is a good means [34]. It was introduced to the finance community by Cont and Bouchaud [17]. It can reproduce well the power-law distribution of the logarithmic returns and some other important stylized facts. After the initial CB model, many studies at “improvements” have tried to get more realistic results or make the model more reasonable [18], [27], [28], [30], [31], [32] and [33]: the activity varies with feedback from the last price [30] and [35] or the size of cluster [27]; the connectivity parameter ranges from 0 to the critical value pcpc [27] and so on. Motivated by the above ideas, we let the connectivity parameter pp vary in a self-organized process and the activity be influenced not only by the last difference between demand and supply but also by the information arriving in the market. Especially, we further depict a detailed process of information transmission and communication among agents. As an open complex system, a financial market exchanges information with its external environment. Then the information, whose secret level and influence will vary over time, spreads along a differentiated path for different interactions between investors. A weighted scale-free network is used to describe heterogeneous interaction among people. As information spreads among people, increasingly investors are attracted to participate in trading and “herd behavior” is magnified gradually, which will induce the topology of the investors’ trade network to change and the price to fluctuate. Compared with other models, our contribution is to describe a microscopic communication process between agents. Fortunately, our improved model will reproduce the non-normal scaling behavior of price fluctuation under different initial conditions and parameters. What’s more, the statistic properties are also very close to the empirical results. The text is organized as follows. Section 2 introduces the details of our model. Section 3 presents detailed analyses. Finally, Section 4 provides our conclusion and outlines some insights.

For the financial market, how stylized facts of price fluctuations are deduced from microscopic interactions among investors is a puzzle in the economic community. Here, incorporating a scale-free network to describe people’s interaction relationship, our improved model not only discloses information asymmetry among agents, but also illustrates a microscopic communication process between agents. Especially it realizes a process that different interactions between investors will prompt information to propagate along differentiated path. As information spreads among people, increasingly investors are attracted to participate in trading, then the “herding effect” is magnified gradually, which will induce market network to change and the price to fluctuate. Especially, under different initial conditions or parameters, the peak and fat-tail property is produced and the statistic values coincide with empirical results: the power-law exponents between the peak value of return probability distribution and the time scales range from 0.579 to 0.747, and that exponents between the accumulation distribution and the return on the tail are close to 3. Besides, the extent of volatility clustering in our produced price series is close to that of S&P 500 and located between NASDAQ and HSI. All the results obtained here indicate that the continuous variation of the “herding effect” resulting from information propagation among interacting investors may be the origin of price fluctuations’ stylized facts. In addition, it also suggests that the variation of topology resulting from the “herding effect” could play a critical role on the volatility. Up to now, there are still many studies trying their best to disclose the relation between people’s behavior and the dynamic of financial time series. The encouraging results mentioned here can provide one with the ability to search for the origin of price fluctuations from the self-organized evolution of the market structure. So investigating the effect of market key structure on price volatility is our future work.