Volatility Effects on the Escape Time in Financial Market Models

We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the effect both of noise and different initial conditions on the escape time in a market model with stochastic volatility and a cubic nonlinearity. For this model we compare the PF of the stock price returns, the PF of the volatility and the return correlation with the same statistical characteristics obtained from real market data.Comment: 12 pages, 9 figures, to appear in Int. J. of Bifurcation and Chaos, 200

Delocalization and conductance quantization in one-dimensional systems

We investigate the delocalization and conductance quantization in finite one-dimensional chains with only off-diagonal disorder coupled to leads. It is shown that the appearence of delocalized states at the middle of the band under correlated disorder is strongly dependent upon the even-odd parity of the number of sites in the system. In samples with inversion symmetry the conductance equals $2e^{2}/h$ for odd samples, and is smaller for even parity. This result suggests that this even-odd behaviour found previously in the presence of electron correlations may be unrelated to charging effects in the sample.Comment: submitted to PR

Optical excitations of Peierls-Mott insulators with bond disorder

The density-matrix renormalization group (DMRG) is employed to calculate optical properties of the half-filled Hubbard model with nearest-neighbor interactions. In order to model the optical excitations of oligoenes, a Peierls dimerization is included whose strength for the single bonds may fluctuate. Systems with up to 100 electrons are investigated, their wave functions are analyzed, and relevant length-scales for the low-lying optical excitations are identified. The presented approach provides a concise picture for the size dependence of the optical absorption in oligoenes.Comment: 12 pages, 13 figures, submitted to Phys. Rev.

Runx1 orchestrates sphingolipid metabolism and glucocorticoid resistance in lymphomagenesis

The three-membered RUNX gene family includes RUNX1, a major mutational target in human leukemias, and displays hallmarks of both tumour suppressors and oncogenes. In mouse models the Runx genes appear to act as conditional oncogenes, as ectopic expression is growth suppressive in normal cells but drives lymphoma development potently when combined with over-expressed Myc or loss of p53. Clues to underlying mechanisms emerged previously from murine fibroblasts where ectopic expression of any of the Runx genes promotes survival through direct and indirect regulation of key enzymes in sphingolipid metabolism associated with a shift in the ‘sphingolipid rheostat’ from ceramide to sphingosine-1-phosphate (S1P). Testing of this relationship in lymphoma cells was therefore a high priority. We find that ectopic expression of Runx1 in lymphoma cells consistently perturbs the sphingolipid rheostat, while an essential physiological role for Runx1 is revealed by reduced S1P levels in normal spleen after partial Cre-mediated excision. Furthermore we show that ectopic Runx1 expression confers increased resistance of lymphoma cells to glucocorticoid-mediated apoptosis, and elucidate the mechanism of cross-talk between glucocorticoid and sphingolipid metabolism through Sgpp1. Dexamethasone potently induces expression of Sgpp1 in T-lymphoma cells and drives cell death which is reduced by partial knockdown of Sgpp1 with shRNA or direct transcriptional repression of Sgpp1 by ectopic Runx1. Together these data show that Runx1 plays a role in regulating the sphingolipid rheostat in normal development and that perturbation of this cell fate regulator contributes to Runx-driven lymphomagenesis

Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations

A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard -- linear Fokker-Planck equation -- may be also related to a family of nonlinear Fokker-Planck equations.Comment: 19 pages, no figure

Pricing Exotic Options in a Path Integral Approach

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances.Comment: 21 pages, LaTeX, 3 figures, 6 table

One Dimensional Chain with Long Range Hopping

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude \expectation{|t_{ij}|} \propto |i-j|^{-\sigma} in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $\sigma$ becomes smaller than 2

Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition

We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as $r^{-\alpha}$. We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, $\nu$ is independent of $\alpha$ but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.Comment: submitted to Phys. Rev. Let

Liquidity and the multiscaling properties of the volume traded on the stock market

We investigate the correlation properties of transaction data from the New York Stock Exchange. The trading activity f(t) of each stock displays a crossover from weaker to stronger correlations at time scales 60-390 minutes. In both regimes, the Hurst exponent H depends logarithmically on the liquidity of the stock, measured by the mean traded value per minute. All multiscaling exponents tau(q) display a similar liquidity dependence, which clearly indicates the lack of a universal form assumed by other studies. The origin of this behavior is both the long memory in the frequency and the size of consecutive transactions.Comment: 7 pages, 3 figures, submitted to Europhysics Letter

Group entropies, correlation laws and zeta functions

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.Comment: to appear in Physical Review