It is well-known that financial asset returns exhibit fat-tailed distributions and long-term memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agent-based simulations to understand the underlying microscopic interactions. After reviewing selected empirical and theoretical evidence documenting the behavior of traders, we construct an agent-based model to quantitatively demonstrate that "fat" tails in return distributions arise when traders share similar technical trading strategies and decisions. Extending our behavioral model to a stochastic model, we derive and explain a set of quantitative scaling relations of long-term memory from the empirical behavior of individual market participants. Our analysis provides a behavioral interpretation of the long-term memory of absolute and squared price returns: They are directly linked to the way investors evaluate their investments by applying technical strategies at different investment horizons, and this quantitative relationship is in agreement with empirical findings. Our approach provides a possible behavioral explanation for stochastic models for financial systems in general and provides a method to parameterize such models from market data rather than from statistical fitting.complex systems | power law | scaling laws M odeling price returns has become a central topic in the study of financial markets due to its key role in financial theory and its practical utility. Following models by Engle and Bollerslev (1, 2), many stochastic models have been proposed based on statistical studies of financial data to accurately reproduce price dynamics. In contrast to this stochastic approach, economists and physicists using the tools of statistical mechanics have adopted a bottom-up approach to simulate the same macroscopic regularity of price changes, with a focus on the behavior of individual market participants (3-10). Although the second socalled agent-based approach has provided a qualitative understanding of price mechanisms, it has not yet achieved sufficient quantitative accuracy to be widely accepted by practitioners.Here, we combine the agent-based approach with the stochastic process approach and propose a model based on the empirically proven behavior of individual market participants that quantitatively reproduces fat-tailed return distributions and long-term memory properties (11-14). Empirical and Theoretical Market BehaviorsWe start by arguing that technical traders (usually agents seeking arbitrage opportunities and make their trading decisions based on price patterns) contribute much more to the dynamics of daily stock prices S t (or log price s t ≡ lnðS t Þ) than fundamentalists (who attempt to determine the fundamental values of stocks). Although fundamentalists hold a majority of the stocks, they trade infrequently (see SI Appendix, Fig. S6). In contrast, technical traders contribute most of the trading activities (15) by trading their minority h...
The 2008–2012 global financial crisis began with the global recession in December 2007 and exacerbated in September 2008, during which the U.S. stock markets lost 20% of value from its October 11 2007 peak. Various studies reported that financial crisis are associated with increase in both cross-correlations among stocks and stock indices and the level of systemic risk. In this paper, we study 10 different Dow Jones economic sector indexes, and applying principle component analysis (PCA) we demonstrate that the rate of increase in principle components with short 12-month time windows can be effectively used as an indicator of systemic risk—the larger the change of PC1, the higher the increase of systemic risk. Clearly, the higher the level of systemic risk, the more likely a financial crisis would occur in the near future.
Modern social media are becoming overloaded with information because of the rapidly-expanding number of information feeds. We analyze the user-generated content in Sina Weibo, and find evidence that the spread of popular messages often follow a mechanism that differs from the spread of disease, in contrast to common belief. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold in contrast to the zero threshold in disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received.
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