Collective behavior of stock prices as a precursor to market crash

We study precursors to the global market crash that occurred on all main stock exchanges throughout the world in October 2008 about three weeks after the bankruptcy of Lehman Brothers Holdings Inc. on 15 September. We examine the collective behavior of stock returns and analyze the market mode, which is a market-wide collective mode, with constituent issues of the FTSE 100 index listed on the London Stock Exchange. Before the market crash, a sharp rise in a measure of the collective behavior was observed. It was shown to be associated with news including the words "financial crisis." They did not impact stock prices severely alone, but they exacerbated the pessimistic mood that prevailed among stock market participants. Such news increased after the Lehman shock preceding the market crash. The variance increased along with the cumulative amount of news according to a power law.Comment: 10 pages, 7 figure

Landau Gauge Fixing supported by Genetic Algorithm

A class of algorithms for the Landau gauge fixing is proposed, which makes the steepest ascent (SA) method be more efficient by concepts of genetic algorithm. Main concern is how to incorporate random gauge transformation (RGT) %, mutation in genetic algorithm (GA) terminology, to gain higher achievement of the minimal Landau gauge fixing, and to keep lower time consumption. One of these algorithms uses the block RGT, and another uses RGT controlled by local fitness density, and the last uses RGT determined by Ising Monte Carlo process. We tested these algorithms on SU(2) lattice gauge theory in 4 dimension with small $\beta$s, 2.0, 1.75 and 1.5, and report improvements in hit rate and/or in time consumption, compared to other methods.Comment: 3 pages, 3 figures LATTICE'99(ALGORITHM

Classical Aspects of the Abelian Higgs Model on the Light Front

We investigate canonical structure of the Abelian Higgs model within the framework of DLCQ. Careful boundary analysis of differential equations, such as the Euler-Lagrange equations, leads us to a novel situation where the canonical structure changes in a drastic manner depending on whether the (light-front) spatial Wilson line is periodic or not. In the former case, the gauge-field ZM takes discrete values and we obtain the so-called ``Zero-Mode Constraints'' (ZMCs), whose semiclassical solutions give a nonzero vev to the scalar fields. Contrary, in the latter case, we have no ZMC and the scalar ZMs remain dynamical as well as the gauge-field ZM. In order to give classically nonzero vev to the scalar field, we work in a background field which minimizes the light-front energy.Comment: 10 pages, reference modifie

The new definition of lattice gauge fields and the Landau gauge

The Landau gauge fixing algorithm in the new definition of gauge fields is presented. In this algorithm a new solver of the Poisson equations based on the Green's function method is used. Its numerical performance of the gauge fixing algorithm is presented. Performance of the smeared gauge fixing in SU(3) is also investigated.Comment: LATTICE98(Algorithms) 3 pages 3, 3 eps figure

CP-Violation in the Renormalizable Theory of Weak Interaction

In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed

Market-wide price co-movement around crashes in the Tokyo Stock Exchange

As described in this paper, we study market-wide price co-movements around crashes by analyzing a dataset of high-frequency stock returns of the constituent issues of Nikkei 225 Index listed on the Tokyo Stock Exchange for the three years during 2007--2009. Results of day-to-day principal component analysis of the time series sampled at the 1 min time interval during the continuous auction of the daytime reveal the long range up to a couple of months significant auto-correlation of the maximum eigenvalue of the correlation matrix, which express the intensity of market-wide co-movement of stock prices. It also strongly correlates with the open-to-close intraday return and daily return of Nikkei 225 Index. We also study the market mode, which is the first principal component corresponding to the maximum eigenvalue, in the framework of Multi-fractal random walk model. The parameter of the model estimated in a sliding time window, which describes the covariance of the logarithm of the stochastic volatility, grows before almost all large intraday price declines of less than -5%. This phenomenon signifies the upwelling of the market-wide collective behavior before the crash, which might reflect a herding of market participants.Comment: 18 pages, 7 figures, to appear in Evolutionary and Institutional Economics Review special issu

Correlation of coming limit price with order book in stock markets

We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price according to a power-law, and it isn't randomly drawn from the distribution, but has a strong correlation with the size of cumulative unexecuted limit orders on the price. It was also found that the limit price, on the coarse-grained price scale, tends to gather around the price which has a large size of cumulative unexecuted limit orders

Custodial SU(2) Violation and the Origin of Fermion Masses

Custodial $SU(2)$ breaking due to dynamical fermion masses is studied in a rather general context and it is shown how some well known limiting cases are correctly described. The type of ``gap equation'' which can systematically lead to extra negative contributions to the so--called $\rho$--parameter is emphasized. Furthermore general model independent features are discussed and it is shown how electro--weak precision measurements can be sensitive to the fermion content and/or dynamical features of a given theory.Comment: HD-THEP-92-55, 18 pages and 2 pages of figures appended as Postscript fil

An operator-theoretical treatment of the Maskawa-Nakajima equation in the massless abelian gluon model

The Maskawa-Nakajima equation has attracted considerable interest in elementary particle physics. From the viewpoint of operator theory, we study the Maskawa-Nakajima equation in the massless abelian gluon model. We first show that there is a nonzero solution to the Maskawa-Nakajima equation when the parameter $\lambda$ satisfies $\lambda>2$. Moreover, we show that the solution is infinitely differentiable and strictly decreasing. We thus conclude that the massless abelian gluon model generates the nonzero quark mass spontaneously and exhibits the spontaneous chiral symmetry breaking when $\lambda>2$. We next show that there is a unique solution $0$ to the Maskawa-Nakajima equation when $0<\lambda<1$, from which we conclude that each quark remains massless and that the model realizes the chiral symmetry when $0<\lambda<1$.Comment: 10 page