Social Simulation of Stock Markets: Taking It to the Next Level

This paper studies the use of social simulation in linking micro level investor behaviour and macro level stock market dynamics. Empirical data from a survey on individual investors\' decision-making and social interaction was used to formalize the trading and interaction rules of the agents of the artificial stock market SimStockExchange. Multiple simulation runs were performed with this artificial stock market, which generated macro level results, like stock market prices and returns over time. These outcomes were subsequently compared to empirical macro level data from real stock markets. Partial qualitative as well as quantitative agreement between the simulated asset returns distributions and the asset returns distributions of the real stock markets was found.Agent-Based Computational Finance, Artificial Stock Markets, Behavioral Finance, Micro-Macro Links, Multi-Agent Simulation, Stock Market Characteristics

Stochastic Opinion Formation in Scale-Free Networks

The dynamics of opinion formation in large groups of people is a complex non-linear phenomenon whose investigation is just at the beginning. Both collective behaviour and personal view play an important role in this mechanism. In the present work we mimic the dynamics of opinion formation of a group of agents, represented by two state $\pm 1$, as a stochastic response of each of them to the opinion of his/her neighbours in the social network and to feedback from the average opinion of the whole. In the light of recent studies, a scale-free Barab\'asi-Albert network has been selected to simulate the topology of the interactions. A turbulent-like dynamics, characterized by an intermittent behaviour, is observed for a certain range of the model parameters. The problem of uncertainty in decision taking is also addressed both from a topological point of view, using random and targeted removal of agents from the network, and by implementing a three state model, where the third state, zero, is related to the information available to each agent. Finally, the results of the model are tested against the best known network of social interactions: the stock market. A time series of daily closures of the Dow Jones index has been used as an indicator of the possible applicability of our model in the financial context. Good qualitative agreement is found.Comment: 24 pages and 13 figures, Physical Review E, in pres

Crashes as Critical Points

We study a rational expectation model of bubbles and crashes. The model has two components : (1) our key assumption is that a crash may be caused by local self-reinforcing imitation between noise traders. If the tendency for noise traders to imitate their nearest neighbors increases up to a certain point called the ``critical'' point, all noise traders may place the same order (sell) at the same time, thus causing a crash. The interplay between the progressive strengthening of imitation and the ubiquity of noise is characterized by the hazard rate, i.e. the probability per unit time that the crash will happen in the next instant if it has not happened yet. (2) Since the crash is not a certain deterministic outcome of the bubble, it remains rational for traders to remain invested provided they are compensated by a higher rate of growth of the bubble for taking the risk of a crash. Our model distinguishes between the end of the bubble and the time of the crash,: the rational expectation constraint has the specific implication that the date of the crash must be random. The theoretical death of the bubble is not the time of the crash because the crash could happen at any time before, even though this is not very likely. The death of the bubble is the most probable time for the crash. There also exists a finite probability of attaining the end of the bubble without crash. Our model has specific predictions about the presence of certain critical log-periodic patterns in pre-crash prices, associated with the deterministic components of the bubble mechanism. We provide empirical evidence showing that these patterns were indeed present before the crashes of 1929, 1962 and 1987 on Wall Street and the 1997 crash on the Hong Kong Stock Exchange. These results are compared with statistical tests on synthetic data.Comment: A total of 40 pages including 9 figures and 6 table

Wealth distribution across communities of adaptive financial agents

This paper studies the trading volumes and wealth distribution of a novel agent-based model of an artificial financial market. In this model, heterogeneous agents, behaving according to the Von Neumann and Morgenstern utility theory, may mutually interact. A Tobin-like tax (TT) on successful investments and a flat tax are compared to assess the effects on the agents' wealth distribution. We carry out extensive numerical simulations in two alternative scenarios: i) a reference scenario, where the agents keep their utility function fixed, and ii) a focal scenario, where the agents are adaptive and self-organize in communities, emulating their neighbours by updating their own utility function. Specifically, the interactions among the agents are modelled through a directed scale-free network to account for the presence of community leaders, and the herding-like effect is tested against the reference scenario. We observe that our model is capable of replicating the benefits and drawbacks of the two taxation systems and that the interactions among the agents strongly affect the wealth distribution across the communities. Remarkably, the communities benefit from the presence of leaders with successful trading strategies, and are more likely to increase their average wealth. Moreover, this emulation mechanism mitigates the decrease in trading volumes, which is a typical drawback of TTs.Comment: 18 pages, 7 figures, published in New Journal of Physic