相关论文: Scaling and correlation in financial data
We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of…
Modelling accurately financial price variations is an essential step underlying portfolio allocation optimization, derivative pricing and hedging, fund management and trading. The observed complex price fluctuations guide and constraint our…
In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the…
The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents.…
In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional…
Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
We study the return interval $\tau$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For…
A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in classical many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$,…
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a…
The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I…
We investigate the dynamics of the out-of-time-ordered correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies $\mathcal{PT}$-symmetry. The spontaneous $\cal{PT}$-symmetry…
We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function…
The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50…
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…
Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena,…
Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management…