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 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.

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.

From the path integral description of price fluctuations with non-Gaussian distributions we derive a stochastic calculus which replaces Itô's calculus for harmonic fluctuations. We set up a natural martingale for option pricing from the wealth balance of options, stocks, and bonds, and evaluate...

From the path integral formalism for price fluctuations with non-Gaussian distributions we derive the appropriate stochastic calculus replacing Itô's calculus for stochastic fluctuations.

Extending recent work on QED and the symmetric phase of the euclidean multicomponent scalar φ4-theory, we construct the vacuum diagrams of the free energy and the effective energy in the ordered phase of φ4-theory. By regarding them as functionals of the free correlation function and the...