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Following the thermodynamic formulation of multifractal measure that was shown to be capable of detecting large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crisis in real…

Specialized topics on financial data analysis from a numerical and physical point of view are discussed. They pertain to the analysis of crash prediction in stock market indices and to the persistence or not of coherent and random sequences…

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well…

The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…

An empirical analysis of interest rates in money and capital markets is performed. We investigate a set of 34 different weekly interest rate time series during a time period of 16 years between 1982 and 1997. Our study is focused on the…

We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the…

We highlight a very simple statistical tool for the analysis of financial bubbles, which has already been studied in [1]. We provide extensive empirical tests of this statistical tool and investigate analytically its link with stocks…

The Sornette-Ide differential equation of herding and rational trader behaviour together with very small random noise is shown to lead to crashes or bubbles where the price change goes to infinity after an unpredictable time. About 100 time…

We exploit a continuous time random walk description of stock prices to obtain a fast and accurate evaluation of their volatility from intraday data. We show that financial markets are usefully described as open physical systems. Indeed we…

We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe…

We propose a reduced form set of two coupled continuous time equations linking the price of a representative asset and the price of a bond, the later quantifying the cost of borrowing. The feedbacks between asset prices and bonds are…

We exploit a recent computational framework to model and detect financial crises in stock markets, as well as shock events in cryptocurrency markets, which are characterized by a sudden or severe drop in prices. Our method manages to detect…

Topological data analysis has been acknowledged as one of the most successful mathematical data analytic methodologies in various fields including medicine, genetics, and image analysis. In this paper, we explore the potential of this…

We select n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We analyze each ensemble of stock returns by…

We study the volatility of the MIB30-stock-index high-frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous-time finance. To this…

We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock…

To uncover underlying mechanism of collective human dynamics, we survey more than 1.8 billion blog entries and observe the statistical properties of word appearances. We focus on words that show dynamic growth and decay with a tendency to…

Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous…

Synchronising a database of stock specific news with 5 years worth of order book data on 300 stocks, we show that abnormal price movements following news releases (exogenous) exhibit markedly different dynamical features from those arising…

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…