In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly...

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the...

It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for v have a specific functional form. Ensuing...

We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the...

In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of R\'{e}nyi's entropy and the mean squared error analysis to...

In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of Rényi’s entropy and the mean squared error analysis to...

In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for...

We provide a unifying axiomatics for Rényi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszár's measure of directed divergence known from communication theory.

We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their admixture to a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the...

Within a path integral formalism for non-Gaussian price fluctuations, we set up a simple stochastic calculus and derive a natural martingale for option pricing from the wealth balance of options, stocks, and bonds. The resulting formula is evaluated for truncated Lèvy distributions.