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The structure and dynamics of complex network systems are of current research interest. We illustrate the dependency between the network topology and its function, considering the complex financial network as a typical example. The networks are built from the full cross-correlation matrix and the global-motion one respectively, aiming at filtering the noise interference of the dynamic networks and understanding the driving mechanism of different interactions. Dynamic structural features of the core and periphery nodes are investigated, and it is demonstrated that the peripherality in a network can be used as an indicator for identifying the optimal assets. With the network filtering approach and peripherality measure, portfolios with different performances are constructed. Compared to the full cross-correlation matrix, the global-motion one shows significant advantages in the portfolio optimization, and the underlying mechanism is carefully analyzed. These methods are also with potential significance to the understanding of other social, biological and transport systems.

As financial derivative products and systemic risk management tools, stock index futures and options have been greatly developed and widely issued in many countries. Taking the Shanghai Stock Exchange 50 (SSE 50) Index and its derivatives as the research objects, we first analyze the lead–lag relationship between stock index, index futures and index options in the Chinese mainland stock market based on a thermal optimal path (TOP) method whose essence is a non-parametric methodology, and compare the results with two mature markets, namely the Hong Kong and US stock markets. We find: (I) In US and Hong Kong stock markets, the index future leads the index. The index option leads the index future when the index remains stable or in an up-trend, but their lead–lag relation reverses when the index collapses; (II) In the Chinese mainland stock market, the index leads the index future, and the index option leads the index future in the whole period of our investigation; (III) In all three markets, the index option leads the index when the index remains stable or in an up-trend, but their lead–lag relation reverses when the index collapses. Our work gives new and strong evidence that the lead–lag relationship varies in different markets and with different market conditions, which has an important contribution to the reveal of the price discovery function of derivative products.

For complex dynamic systems in non-stationary states, we develop a useful method to simplify the calculation of time correlations. The method is particularly applied to the financial dynamic systems, with focus on how the past fluctuation drives the future motion of the dynamic variables. The results are important both theoretically and practically. Further, we demonstrate how to construct an investment strategy based on the time correlations.

With the natural language processing technique, we quantitatively measure the sentiment expressed in analyst reports of stock markets. Both the analyst sentiment and the earning forecast biases decrease with the fiscal month. The temporal variation of the earning forecast biases displays an asymmetric behavior, i.e., underestimated initial biases may be corrected by the wisdom of crowds, while overestimated ones could not. The Pearson correlation between the analyst sentiment and the earning forecast errors becomes positive, when approaching the end of the fiscal year. In addition, the analyst sentiment is different from the common investor sentiment.

Exploring the scientific impact of online big-data has attracted much attention of researchers from different fields in recent years. Complex financial systems are typical open systems profoundly influenced by the external information. Based on the large-scale data in the public media and stock markets, we first define an information driving force, and analyze how it affects the complex financial system. The information driving force is observed to be asymmetric in the bull and bear market states. As an application, we then propose an agent-based model driven by the information driving force. Especially, all the key parameters are determined from the empirical analysis rather than from statistical fitting of the simulation results. With our model, both the stationary properties and non-stationary dynamic behaviors are simulated. Considering the mean-field effect of the external information, we also propose a few-body model to simulate the financial market in the laboratory.

With data from epitaphs of elites in ancient China, we construct the elite social networks of the Tang-dynasty and the Song-dynasty. The complexity theory is then introduced to unveil associations between the elite social networks and the history. The top influential elites in ancient China are identified from the elite social networks. We detect the community structure formed with strongly connected elites, and investigate the interactions between the communities. It is observed that the elite social networks of the Tang-dynasty and the Song-dynasty exhibit the neutral and disassortative mixing patterns, respectively. Additionally, this work quantitatively supports the Tang-Song Transition Hypothesis.

How trading volume responds to price return is investigated by the return–volume correlation dynamics, based on the daily data of two typical financial markets, i.e., the Chinese and the United States stock markets. Whereas the price returns being observed to be positively correlated with the trading volumes for the Chinese stock markets, a significant transition from the positive correlation to negative correlation is revealed for the United States stock markets. Leverage and anti-leverage effects of the return–volume correlations are found for the last decade of the United States stock markets and the Chinese stock markets, respectively. Nonlocal dynamics further suggests an adverse correlation for the two markets. A retarded herding model is introduced to describe the leverage and anti-leverage effects. Our work may shed a new light on the financial dynamics differing in the mature and emerging markets.