Some Applications Of Random Matrices In Financial Stocks

The thesis studys the influence of the economic crisis on the financial stock market. by applying the method of random matrix theory. The time we selected is from January4,2007to December31,2009. The objects of study are A and B shares of dual-listed compa-nies in Shenzhen Stock Exchange, each totaling of41. In this paper, we use the method of Pearson correlation coefficient to construct A, B shares correlation coefficient matrix. By studying their eigenvalues, the correlation coefficient and the statistical properties of the eigenvectors, we research the similarities and differences between A and B shares dynami-cally. The dynamic embodies in three aspects:firstly, when we study the instability of A, B shares, we choose the time window by T=20slidly, once slip19days backward, so A, B shares produce38time quantums eath, we analysis the instability of A, B shares in these periods. Secondly, when we discuss the change trend of λmax,<Cij> with v(t), we choose the time window by T=100slidly, each time glide1day back, so A, B shares produce633time periods eath, we calculate the maximum eigenvalue and the average correlation coefficient of A, B shares in these periods, when we calculate v(t), we choose T=2, once slide1day backward too, producing731periods, thus we compare the relationship among the three variables on the same graph. When we study the relevance between eigenvalue and correlation coefficient, we elect T=183, every time slide10days back, producing55periods, accordingly with55matrixes. When we analysis the stability of the eigenvector, we also select T=232, once glide99days back, producing5periods, accordingly with5matrixes. Thirdly, we choose four representative periods for A and B shares, discuss the distribution of the eigenvector corresponding to the maximum eigenvalue.At last, we conlude that:first, we find the price of A shares is higher than B share which may be A is relatively perfect in the share market and the investors of A are more. Next, A, B dual listed shares have similar movement trend with market fluctuations, but B shares have more sensitive reactions, so B shares are weak response to market crisis Last, the largest eigenvalue and the corresponding eigenvector influence the market on the whole, and the later has stability. These results can help investors enhance understanding of the stock market, allocate funds reasonably, reduce risk and increase income.