Related papers: Financial Market Dynamics: Superdiffusive or not?
We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the…
A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent close to 3. We revisit this results and use standard tests as well as develop a…
We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…
The probability distribution of log-returns for financial time series, sampled at high frequency, is the basis for any further developments in quantitative finance. In this letter, we present experimental results based on a large set of…
We recently showed that the S&P500 stock market index is well described by Tsallis non-extensive statistics and nonlinear Fokker-Planck time evolution. We argued that these results should be applicable to a broad range of markets and…
In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or…
We study the evolution of probability distribution functions of returns, from the tick data of the Korean treasury bond (KTB) futures and the S$&$P 500 stock index, which can be described by means of the Fokker-Planck equation. We show that…
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…
We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
We present the qGaussian generalization of the Merton framework, which takes into account slow fluctuations of the volatility of the firms market value of financial assets. The minimal version of the model depends on the Tsallis entropic…
The stochastic properties of variables whose addition leads to $q$-Gaussian distributions $G_q(x)=[1+(q-1)x^2]_+^{1/(1-q)}$ (with $q\in\mathbb{R}$ and where $[f(x)]_+=max\{f(x),0\}$) as limit law for a large number of terms are…
Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across…
The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined…
We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average…
We developed a strategic of optimal portfolio based on information theory and Tsallis statistics. The growth rate of a stock market is defined by using $q$-deformed functions and we find that the wealth after n days with the optimal…
We present a new framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the nonextensive thermostatistics proposed by Tsallis. We also show that intermittency…
We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs…
Option pricing formulas are derived from a non-Gaussian model of stock returns. Fluctuations are assumed to evolve according to a nonlinear Fokker-Planck equation which maximizes the Tsallis nonextensive entropy of index $q$. A generalized…
The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole…