No Arabic abstract
In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, whereas news tend on average to be followed by lower volatility levels. The shape of the volatility relaxation is also markedly different in the two cases. Finally, we provide direct evidence that large transaction volumes are_not_ responsible for large price jumps. We conjecture that most price jumps are induced by order flow fluctuations close to the point of vanishing liquidity.
We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex systems by identifying three of them on real-life financial markets. We extract and interpret the empirical, numerical, and semi-analytical evidences for the existence of these phase transitions, by considering the Frankfurt Stock Exchange (FSE), as a typical example of a financial market of a medium size. Using the canonical object for the graph theory, i.e. the Minimal Spanning Tree (MST) network, we observe: (i) The initial phase transition from the equilibrium to non-equilibrium MST network in its nucleation phase, occurring at some critical time. Coalescence of edges on the FSEs transient leader is observed within the nucleation and is approximately characterized by the Lifsthiz-Slyozov growth exponent; (ii) The nucleation accelerates and transforms to the condensation process, in the second phase transition, forming a logarithmically diverging lambda-peak of short-range order parameters at the subsequent critical time - an analogon of such a transition in superfluidity; (iii) In the third phase transition, the peak logarithmically decreases over three quarters of the year, resulting in a few loosely connected sub-graphs. This peak is reminiscent of a non-equilibrium superstar-like superhub or a `dragon king effect, abruptly accelerating the evolution of the leader company. All these phase transitions are caused by the few richest vertices, which drift towards the leader and provide the most of the edges increasing the leaders degree. Thus, we capture an amazing phenomenon, likely of a more universal character, where a peripheral vertex becomes the one which is over dominating the complex network during an exceptionally long period of time.
We propose a novel method to quantify the clustering behavior in a complex time series and apply it to a high-frequency data of the financial markets. We find that regardless of used data sets, all data exhibits the volatility clustering properties, whereas those which filtered the volatility clustering effect by using the GARCH model reduce volatility clustering significantly. The result confirms that our method can measure the volatility clustering effect in financial market.
Using a recently introduced method to quantify the time varying lead-lag dependencies between pairs of economic time series (the thermal optimal path method), we test two fundamental tenets of the theory of fixed income: (i) the stock market variations and the yield changes should be anti-correlated; (ii) the change in central bank rates, as a proxy of the monetary policy of the central bank, should be a predictor of the future stock market direction. Using both monthly and weekly data, we found very similar lead-lag dependence between the S&P500 stock market index and the yields of bonds inside two groups: bond yields of short-term maturities (Federal funds rate (FFR), 3M, 6M, 1Y, 2Y, and 3Y) and bond yields of long-term maturities (5Y, 7Y, 10Y, and 20Y). In all cases, we observe the opposite of (i) and (ii). First, the stock market and yields move in the same direction. Second, the stock market leads the yields, including and especially the FFR. Moreover, we find that the short-term yields in the first group lead the long-term yields in the second group before the financial crisis that started mid-2007 and the inverse relationship holds afterwards. These results suggest that the Federal Reserve is increasingly mindful of the stock market behavior, seen at key to the recovery and health of the economy. Long-term investors seem also to have been more reactive and mindful of the signals provided by the financial stock markets than the Federal Reserve itself after the start of the financial crisis. The lead of the S&P500 stock market index over the bond yields of all maturities is confirmed by the traditional lagged cross-correlation analysis.
In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix. We determined that the value of the eigenvalue increases in proportion with the number of stocks. Furthermore, we noted that the largest eigenvalue maintains its identical properties, regardless of the number and type, whereas other eigenvalues evidence different features.
We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-balance condition necessary for equilibrium in the Ehrenfest-Brillouin model. We also carry out an empirical analysis on the average number of workers in given productivity sectors on the basis of an exhaustive dataset in Japan. The theoretical formula succeeds in explaining the two distinctive observational facts in a unified way, that is, a Boltzmann distribution with negative temperature on low-to-medium productivity side and a decreasing part in a power-law form on high productivity side.