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Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations

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  • Vinogradov, Dmitry V.

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.

Suggested Citation

  • Vinogradov, Dmitry V., 2012. "Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5584-5597.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5584-5597
    DOI: 10.1016/j.physa.2012.06.022
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    References listed on IDEAS

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    1. Vinogradov, Dmitry V., 2010. "Cumulant approach of arbitrary truncated Levy flight," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5794-5800.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. Edward I. Altman, 1968. "Financial Ratios, Discriminant Analysis And The Prediction Of Corporate Bankruptcy," Journal of Finance, American Finance Association, vol. 23(4), pages 589-609, September.
    4. repec:bla:joares:v:22:y:1984:i::p:59-82 is not listed on IDEAS
    5. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    6. Dmitry V. Vinogradov, 2010. "Cumulant Approach of Arbitrary Truncated Levy Flight," Papers 1006.2489, arXiv.org, revised Oct 2010.
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