Scaling and efficiency determine the irreversible evolution of a market

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficiency and on an inhomogeneous-time generalization of standard simple scaling, we propose an analytical model which accounts simultaneously for empirical results like the linear decorrelation of successive returns, the power law dependence on time of the volatility autocorrelation function, and the multiscaling associated to this dependence. In addition, our approach gives a justification and a quantitative assessment of the irreversible character of the index dynamics. This irreversibility enters as a key ingredient in a novel simulation strategy of index evolution which demonstrates the predictive potential of the model.Comment: 5 pages, 4 figure

Export dynamics as an optimal growth problem in the network of global economy

We analyze export data aggregated at world global level of 219 classes of products over a period of 39 years. Our main goal is to set up a dynamical model to identify and quantify plausible mechanisms by which the evolutions of the various exports affect each other. This is pursued through a stochastic differential description, partly inspired by approaches used in population dynamics or directed polymers in random media. We outline a complex network of transfer rates which describes how resources are shifted between different product classes, and determines how casual favorable conditions for one export can spread to the other ones. A calibration procedure allows to fit four free model-parameters such that the dynamical evolution becomes consistent with the average growth, the fluctuations, and the ranking of the export values observed in real data. Growth crucially depends on the balance between maintaining and shifting resources to different exports, like in an explore-exploit problem. Remarkably, the calibrated parameters warrant a close-to-maximum growth rate under the transient conditions realized in the period covered by data, implying an optimal self organization of the global export. According to the model, major structural changes in the global economy take tens of years

Finite-size scaling in unbiased translocation dynamics

Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for the probability density function of the chemical coordinate matches the initial-stage subdiffusive regime and takes into account the equilibrium entropic drive. Precise scaling relations connect the subdiffusion exponent to the divergence with the polymer length of the translocation time, and also to the singularity of the probability density function at the absorbing boundaries. Quantitative comparisons with numerical simulation data in $d=2$ strongly support the validity of the model and of the predicted scalings.Comment: Text revision. Supplemental Material adde

Scaling symmetry, renormalization, and time series modeling

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous auto-regressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance in terms of obtaining closed formulas for derivative pricing. Further important features are: The possibility of making contact, in certain limits, with auto-regressive models widely used in finance; The possibility of partially resolving the long-memory and short-memory components of the volatility, with consistent results when applied to historical series.Comment: Main text (17 pages, 13 figures) plus Supplementary Material (16 pages, 5 figures

Rayleigh-Benard convection in limited domains: Part 2 - Transition to chaos

Transitions to chaos in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, have been examined by direct numerical simulation as the Rayleigh number is varied. Two different problems have been considered: the first is related to a domain 3.5 X 1 X 2.1 filled with water at 70°C (Prandtl number 2.5); the second is related to a domain 2.4 X 1 X 1.2 filled with water at 33°C (Prandtl number 5). The Rayleigh number has been varied from 45,000 up to 300,000. Three different bifurcation sequences have been detected, but only two individual mechanisms for the transition to the nonperiodic motion have been identified: the subharmonic cascade and the quasi-periodicity with three incommensurate frequencies. Effects of different regimes and flow structures on heat transfer have been discussed

Rayleigh-Benard convection in limited domains: Part 1 - Oscillatory flow

Transition from the steady state to an oscillatory regime in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, has been examined by direct numerical simulation. Two different physical problems have been considered: the first is related to a domain 3.5 X 1 X 2.1 filled with water at 70° C (Prandtl number 2.5); the second considers a domain 2.4 X1 X1.2 filled with water at 33°C (Prandtl number 5). The Rayleigh number has been varied from 20,000 to 80,000. A new procedure based on a statistical approach for ev aluation of the critical Rayleigh number for transition from steady state to oscillatory flow Ra has been introduced in order to reduce numerical errors and estimate the error bars. A systematic study for the determination of Ra has been conducted as a function of the geometries considered and the different flow structures observed

Option pricing with non-Gaussian scaling and infinite-state switching volatility

Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures the above stylized facts, we derive closed form equations for option pricing, obtaining the Black & Scholes as a special case. By applying our pricing equations to a major equity index option dataset, we show that inclusion of stylized features in financial modeling moves derivative prices about 30% closer to the market values without the need of calibrating models parameters on available derivative prices.Comment: Revised version. 31 pages, 4 figure

Aftershock prediction for high-frequency financial markets' dynamics

The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low frequency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited predictive power in this phenomenological approach and present a stochastic model, based on the scaling symmetry of financial assets, which is potentially capable to predict aftershocks occurrence, given the main shock magnitude. Comparisons with S&P high-frequency data confirm this predictive potential.Comment: Contribution to the proceedings of the Econophysics Kolkata VI International Workshop, 12 pages, 4 figures. Added references and minor correction

A partition method for the solution of coupled liquid-structure interaction problem

A numerical code is presented to study the motion of an incompressible inviscid flow in a deformable tank. It is based on a method belonging to the partition treatment class, as the fluid and structural fields are solved by coupling two distinct models. The fluid field is modeled by the Laplace equation and numerically solved by a Finite Volume technique. The computational grid is updated at each time step to take into account the movements of the free surface and the deformations of the vertical walls. An unsteady finite element formulation is used for modeling the tank on a grid discretized by triangular elements and linear shape functions. Results are presented for two different cases: a flow induced by a perturbation on the free surface in a tank motionless; a flow in a tank forced to oscillate periodically in the horizontal direction