Spatio-temporal Correlations In Financial Dynamics Of Chinese And Western Markets

Financial markets are complex systems with many-body interactions similar to those in traditional physics. The advancement of information processing techniques and the achievement of physics in the past 30 years have spurred the interest of physicists to apply physical concepts and methods to analyze financial dynamics. So far, several "stylized facts" of financial markets are revealed and different models have been proposed to reproduce the features of the financial dynamics. The spatio-temporal correlation in financial dynamics is an important topic in econophysics. It not only quantitatively describes the structure and dynamics of financial markets, but also has great influence on the development of financial theory and applications in finance. In this dissertation, we analyze and simulate the spatio-temporal correlations in stock markets, and pay particular attention to the comparative study of Chinese and western markets.In Chapter 1, we first give a brief introduction to the history and current status of financial markets, especially its main component—the stock market. Since the Chinese market has been one of the most important emerging markts in the world, we will take it as our main research objcet. We then introduce the origination, achievements and main research fields of the new interdisciplinary subject: EconoPhysics.In Chapter 2, we selectively give an overview of the progress in EconoPhysics in the recent ten years, including the phenomenological analysis and multi-agent models. Based on empirical analyses, the econophysicists find that the probability distribution of price returns is apparently different from a Gaussian distribution which is the hypothesis in traditional finance; although the price return is short-range correlated in time, the volatility exhibits a long-range temporal correlation; the dynamic behavior of the persistence probability which is non-local in time is characterized by a power law. Econophysicists have proposed various models, especially the multi-agent models, to reproduce the features of the financial dynamics. Two of the most important multi-agent models are the herding model and minority game.In Chapter 3, we analyze the cross-correlation, i.e., the "spatial" correlation, in the Chinese stock market, in comparison with that of the American and Indian stock markets. The average value of the elements of the cross-correlation matrix C for the SSE (China) is much larger than those for the NSE (Indian) and NYSE (USA). In this sense, the Chinse markt is a better representative of emerging markets. We then diagonalize the matrix C and obtain the eigenvalue spectrum and eigenvectors. The large eigenvalues which go beyond the upper bound of the random matrix, i.e., the Wishart matrix, reflect the local correlations between stocks. The largest eigenvalue corresponds to the market mode, and next large eigenvalues represent the interactions between stocks in a same sector. For the NYSE (USA), the correlations corresponding to standard business sectors are strong, and at least 10 such large eigenvalues are identified. For emerging markets such as the SSE (China) and NSE (India), the correlations between stocks in a same business sector are weak. Especially, the correlations within a standard business sector in SSE (China) are almost invisible. But the large eigenvalues indeed exist, and they should correspond to some "sectors". For the SSE (China), we introduce a threshold to identify the sectors, and find that the large eigenvalues correspond to unusual sectors such as the ST and Blue-chip sectors. Finally we apply a variation of the two-factor dynamic model to explain the collective behavior of the Chinese stock market.In Chapter 4, based on the data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. With the retarded volatility model, we can eliminate or generate the leverage effect of the German DAX and anti-leverage effect of the Chinese indices on both daily and minutely time scales, while other characteristics of the time series, such as the probability distribution of returns, time-correlation and persistence probability of returns and volatilities etc., remain essentially unchanged. In addition, the probability distribution of price returns of the German DAX and Chinese indices are not asymmetric before and after eliminating the leverage or anti-leverage effect. These results suggest that at least for the German DAX and Chinese indices, the leverage or anti-leverage effect in financial markets arises from a kind of feedback return-volatility interactions, rather than the long-range time-correlation of volatilities and asymmetric probability distribution of price returns. Finally, we show that the leverage effect of the German DAX and anti-leverage effect of the Chinese indices are dominated by large volatilities.In Chapter 5, based on the data of the German DAX, we investigate the financial dynamics both before and after a large price-change (a large volatility). The dynamic behavior of the remanent and anti-remanent volatility m±(t) is characterized by a power law. The physical origin of the power-law behavior is the long-range temporal correlation of volatilities. It is observed that the dynamic behavior of the daily data before and after a large price-change is asymmetric in time, while that of the minutely data is symmetric. By numerical simulations, we find that the interacting EZ herding model qualitatively reproduces the dynamic behavior of the minutely data in real markets.