Arbitrary Truncated Levy Flight: Asymmetrical Truncation and High-Order Correlations

TL;DR

This paper explores the properties of asymmetrically truncated Levy flights, revealing that non-Gaussian features like skewness and kurtosis induce high-order correlations in these stochastic processes.

Contribution

It introduces a generalized correlation approach to describe non-Gaussian random walks with asymmetrical truncation and investigates the resulting high-order correlations.

Findings

High-order correlations exist in asymmetrically truncated Levy flights.

Skewness leads to threefold correlations.

Kurtosis results in fourfold correlations.

Abstract

The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically distributed increments in the general case, and high-order correlations have been investigated. The cumulants of an asymmetrically truncated Levy distribution have been found. The behaviors of asymmetrically truncated Levy flight, as a particular case of a random walk, are considered. It is shown that, in the Levy regime, high-order correlations between values of asymmetrically truncated Levy flight exist. The source of high-order correlations is the non-Gaussianity of the increments: the increment skewness generates threefold correlation, and the increment kurtosis generates fourfold correlation.