Tick size and price diffusion

A tick size is the smallest increment of a security price. It is clear that at the shortest time scale on which individual orders are placed the tick size has a major role which affects where limit orders can be placed, the bid-ask spread, etc. This is the realm of market microstructure and there is a vast literature on the role of tick size on market microstructure. However, tick size can also affect price properties at longer time scales, and relatively less is known about the effect of tick size on the statistical properties of prices. The present paper is divided in two parts. In the first we review the effect of tick size change on the market microstructure and the diffusion properties of prices. The second part presents original results obtained by investigating the tick size changes occurring at the New York Stock Exchange (NYSE). We show that tick size change has three effects on price diffusion. First, as already shown in the literature, tick size affects price return distribution at an aggregate time scale. Second, reducing the tick size typically leads to an increase of volatility clustering. We give a possible mechanistic explanation for this effect, but clearly more investigation is needed to understand the origin of this relation. Third, we explicitly show that the ability of the subordination hypothesis in explaining fat tails of returns and volatility clustering is strongly dependent on tick size. While for large tick sizes the subordination hypothesis has significant explanatory power, for small tick sizes we show that subordination is not the main driver of these two important stylized facts of financial market.Comment: To be published in the "Proceedings of Econophys-Kolkata V International Workshop on "Econophysics of Order-driven Markets" March 9-13, 2010, The New Economic Windows series of Springer-Verlag Italia

Unbiased, optimal, and in-betweens: the trade-off in discrete finite impulse response filtering

In this survey, the authors examine the trade-off between the unbiased, optimal, and in-between solutions in finite impulse response (FIR) filtering. Specifically, they refer to linear discrete real-time invariant state-space models with zero mean noise sources having arbitrary covariances (not obligatorily delta shaped) and distributions (not obligatorily Gaussian). They systematically analyse the following batch filtering algorithms: unbiased FIR (UFIR) subject to the unbiasedness condition, optimal FIR (OFIR) which minimises the mean square error (MSE), OFIR with embedded unbiasedness (EU) which minimises the MSE subject to the unbiasedness constraint, and optimal UFIR (OUFIR) which minimises the MSE in the UFIR estimate. Based on extensive investigations of the polynomial and harmonic models, the authors show that the OFIR-EU and OUFIR filters have higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters

The Majorana Neutrino Mass Matrix with One Texture Zero and One Vanishing Eigenvalue

Possible patterns of the Majorana neutrino mass matrix $M$ with one texture zero and one vanishing eigenvalue are classified and discussed. We find that three one-zero textures of $M$ with $m_1 =0$ and four one-zero textures of $M$ with $m_3 =0$ are compatible with current neutrino oscillation data. The implications of these phenomenological ans$\rm\ddot{a}$tze on the neutrino mass spectrum and the neutrinoless double beta decay are also explored in some detail.Comment: RevTex 10 pages (with 2 PS figues). More discussions and references adde

Implications of the KamLAND Measurement on the Lepton Flavor Mixing Matrix and the Neutrino Mass Matrix

We explore some important implications of the KamLAND measurment on the lepton flavor mixing matrix $V$ and the neutrino mass matrix $M$. The model-independent constraints on nine matrix elements of $V$ are obtained to a reasonable degree of accuracy. We find that nine two-zero textures of $M$ are compatible with current experimental data, but two of them are only marginally allowed. Instructive predictions are given for the absolute neutrino masses, Majorana phases of CP violation, effective masses of the tritium beta decay and neutrinoless double beta decay.Comment: RevTex 15 pages (4 PS figures included

Vanishing Effective Mass of the Neutrinoless Double Beta Decay?

We stress that massive neutrinos may be Majorana particles even if the effective mass of the neutrinoless double beta decay m_ee vanishes. We show that current neutrino oscillation data do allow m_ee = 0 to hold, if the Majorana CP-violating phases lie in two specific regions. Strong constraints on three neutrino masses can then be obtained. We find that the neutrino mass spectrum performs a normal hierarchy: m_1 < m_2 < m_3. A possible texture of the neutrino mass matrix is also illustrated under the m_ee = 0 condition.Comment: RevTex 9 pages (2 PS figures included). More discussions and references added. Results partly changed. To appear in Phys. Rev.

Radiative Corrections to Neutrino Mixing and CP Violation in the Minimal Seesaw Model with Leptogenesis

Radiative corrections to neutrino mixing and CP violation are analyzed in the minimal seesaw model with two heavy right-handed neutrinos. We find that textures of the effective Majorana neutrino mass matrix are essentially stable against renormalization effects. Taking account of the Frampton-Glashow-Yanagida ansatz for the Dirac neutrino Yukawa coupling matrix, we calculate the running effects of light neutrino masses, lepton flavor mixing angles and CP-violating phases for both $m_1 =0$ (normal mass hierarchy) and $m_3 =0$ (inverted mass hierarchy) cases in the standard model and in its minimal supersymmetric extension. Very instructive predictions for the cosmological baryon number asymmetry via thermal leptogenesis are also given with the help of low-energy neutrino mixing quantities.Comment: 21 pages, 6 figures; more references adde

Measurement of single pi0 production in neutral current neutrino interactions with water by a 1.3 GeV wide band muon neutrino beam

Neutral current single pi0 production induced by neutrinos with a mean energy of 1.3 GeV is measured at a 1000 ton water Cherenkov detector as a near detector of the K2K long baseline neutrino experiment. The cross section for this process relative to the total charged current cross section is measured to be 0.064 +- 0.001 (stat.) +- 0.007 (sys.). The momentum distribution of produced pi0s is measured and is found to be in good agreement with an expectation from the present knowledge of the neutrino cross sections.Comment: 6 pages, 4 figures, Submitted to Phys. Lett.

Tracking Performance of the Scintillating Fiber Detector in the K2K Experiment

The K2K long-baseline neutrino oscillation experiment uses a Scintillating Fiber Detector (SciFi) to reconstruct charged particles produced in neutrino interactions in the near detector. We describe the track reconstruction algorithm and the performance of the SciFi after three years of operation.Comment: 24pages,18 figures, and 1 table. Preprint submitted to NI

Exploring flavor structure of supersymmetry breaking from rare B decays and unitarity triangle

We study effects of supersymmetric particles in various rare B decay processes as well as in the unitarity triangle analysis. We consider three different supersymmetric models, the minimal supergravity, SU(5) SUSY GUT with right-handed neutrinos, and the minimal supersymmetric standard model with U(2) flavor symmetry. In the SU(5) SUSY GUT with right-handed neutrinos, we consider two cases of the mass matrix of the right-handed neutrinos. We calculate direct and mixing-induced CP asymmetries in the b to s gamma decay and CP asymmetry in B_d to phi K_S as well as the B_s--anti-B_s mixing amplitude for the unitarity triangle analysis in these models. We show that large deviations are possible for the SU(5) SUSY GUT and the U(2) model. The pattern and correlations of deviations from the standard model will be useful to discriminate the different SUSY models in future B experiments.Comment: revtex4, 36 pages, 10 figure

Search for Charmless Two-body Baryonic Decays of B Mesons

We report the results of a search for the rare baryonic decays $B^0 \to p\bar{p}$, $\Lambda\bar{\Lambda}$, and $B^+ \to p\bar{\Lambda}$. The analysis is based on a data set of $31.7\times 10^6 B\bar{B}$ events collected by the Belle detector at the KEKB $e^+e^-$ collider. No statistically significant signals are found, and we set branching fraction upper limits ${\mathcal B}(B^0 \to p\bar{p}) < 1.2 \times 10^{-6}$, ${\mathcal B}(B^0 \to \Lambda\bar{\Lambda}) < 1.0 \times 10^{-6}$, and ${\mathcal B}(B^+ \to p\bar{\Lambda}) < 2.2 \times 10^{-6}$ at the 90% confidence level.Comment: 6 pages, 4 figures and 1 table. Submitted to Phys. Rev. D Rapid Communication