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.

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...

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.

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

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...

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...

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...