Cross-correlation in financial dynamics

– To investigate the universal structure of interactions in financial dynamics, we analyze the cross-correlation matrix C of price returns of the Chinese stock market, in comparison with those of the American and Indian stock markets. As an important emerging market, the Chinese market exhibits much stronger correlations than the developed markets. In the Chinese market, the interactions between the stocks in a same business sector are weak, while extra interactions in unusual sectors are detected. Using a variation of the two-factor model, we simulate the interactions in financial markets. In recent years, there has been a growing interest of physicists in economic systems. Concepts and methods in physics have been applied to the study of financial time series [1–7]. Different models and theoretical approaches have been developed to describe the features of the financial dynamics [8–19]. Statistical properties of price fluctuations and correlations between different stocks are topics of interest, not only scientifically for understanding the complex structure and dynamics of the economy, but also practically for the asset allocation and portfolio risk estimation [20–22]. The probability distributions of stock prices in different stock markets show a universal nature and follow the ”inverse cubic law” [23–25]. However, the statistical properties of correlations between different stocks seem less universal across different stock markets [26]. Unlike most traditional physical systems, where one derives correlations between subunits from their interactions, the underlying ”interactions” for the stock markets are not known. Pioneering studies at the phenomenological level analyze cross-correlations between stocks by applying concepts and methods of the random matrix theory (RMT), which was developed in the context of complex quantum systems where the precise nature of the interactions between subunits is not known [27, 28]. The properties of the empirical correlation matrix C of price returns are compared with those of a random matrix in which the price movements are uncorrelated [29, 30]. This spectral property-focused method was first applied to developed markets such as the New York Stock Exchange (NYSE) in USA [29–32], and recently also to some emerging markets, e.g. the National Stock Exchange (NSE) in India [26]. In general, the bulk of the eigenvalue spectrum of the correlation matrix C of price returns shares universal properties with the Gaussian orthogonal ensemble of random matrices, while the largest eigenvalue ofC which deviates significantly from the bulk represents the influence of (∗) corresponding author; email: [email protected]