| The first focus of this thesis is the investigation of cross-correlations between the price fluctuations of different stocks using the conceptual framework of random matrix theory (RMT), developed in physics to describe the statistical properties of energy-level spectra of complex nuclei. RMT makes predictions for the statistical properties of matrices that are universal, i.e., do not depend on the interactions between the elements comprising the system. In physical systems, deviations from the predictions of RMT provide clues regarding the mechanisms controlling the dynamics of a given system so this framework is of potential value if applied to economic systems. This thesis compares the statistics of cross-correlation matrix C—whose elements Cij are the correlation coefficients of price fluctuations of stock i and j—against the “null hypothesis” of a random matrix having the same symmetry properties. It is shown that comparison of the eigenvalue statistics of C with RMT results can be used to distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine cross-correlations between stocks. The interpretations and potential practical utility of these deviations are also investigated.; The second focus is the characterization of the dynamics of stock price fluctuations. The statistical properties of the changes G Δt in price over a time interval Δ t are quantified and the statistical relation between G Δt and the trading activity—measured by the number of transactions NΔ t in the interval Δt is investigated. The statistical properties of the volatility, i.e., the time dependent standard deviation of price fluctuations, is related to two microscopic quantities: NΔt and the variance of the price changes for all transactions in the interval Δ t. In addition, the statistical relationship between G Δt and the number of shares QΔt traded in Δ t is investigated. |
