Related papers: Scaling transformation and probability distributio…
There is a large body of work, built on tools developed in mathematics and physics, demonstrating that financial market prices exhibit self-similarity at different scales. In this paper, we explore the use of analytical topology to…
Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return…
By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche B\"orse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic…
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability…
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the…
Permutation approach is suggested as a method to investigate financial time series in micro scales. The method is used to see how high frequency trading in recent years has affected the micro patterns which may be seen in financial time…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
Multifractal scaling has been extensively studied for real-valued stochastic processes, but a systematic integer-valued analogue has remained largely unexplored. In this work, we introduce a multifractal framework for integer-valued…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking…
We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
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…
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…