Related papers: Dynamic Hurst Exponent in Time Series
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
A new concept, called balanced estimator of diffusion entropy, is proposed to detect scalings in short time series. The effectiveness of the method is verified by means of a large number of artificial fractional Brownian motions. It is used…
The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of…
Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of…
In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of…
Metastability is a phenomenon observed in stochastic systems which stay in a false-equilibrium within a region of its state space until the occurrence of a sequence of rare events that leads to an abrupt transition to a different region.…
Financial markets typically exhibit dynamically complex properties as they undergo continuous interactions with economic and environmental factors. The Efficient Market Hypothesis indicates a rich difference in the structural complexity of…
In this paper we introduce a simple model for a financial market characterized by a single stock or good and an interplay between two different traders populations, chartists and fundamentalists, which determine the price dynamic of the…
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using…
We conclude from an analysis of high resolution NYSE data that the distribution of the traded value $f_i$ (or volume) has a finite variance $\sigma_i$ for the very large majority of stocks $i$, and the distribution itself is non-universal…
We examine Kreps' (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that "approach" the BSM economy in a…
We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients…
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…
We present evidence, that if a large enough set of high resolution stock market data is analyzed, certain analogies with physics -- such as scaling and universality -- fail to capture the full complexity of such data. Despite earlier…
In this paper we seek to demonstrate the predictability of stock market returns and explain the nature of this return predictability. To this end, we introduce investors with different investment horizons into the news-driven, analytic,…
In the present work we investigate the multiscale nature of the correlations for high frequency data (1 minute) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December…
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the…
The multifractal structure of the temporal dependence of the Deutsche Aktienindex (DAX) is analyzed. The $q$-th order moments of the structure functions and the singular measures are calculated. The generalized Hurst exponent $H(q)$ and the…