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A model-free, non-parametric method for density determination, with application to asset returns

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  • Gzyl, Henryk
  • ter Horst, Enrique
  • Molina, Germán

Abstract

The distribution of the returns of an asset is still an open problem despite the variety of models and methods devised to deal with it. In this note we propose a model-free, nonparametric method for the estimation of asset returns, which is applicable also to a wider set of similar problems. The Laplace transform of a shifted rate of return or other percent change of a positive random variables can be transformed into a fractional moment problem which can then be solved by the method of maximum entropy. This is a very robust method and requires only a few values of the Laplace transform to provide good reconstructions. This method can be applied in multiple fields where model-free density estimation of functionals like percent changes of random variables is of interest.

Suggested Citation

  • Gzyl, Henryk & ter Horst, Enrique & Molina, Germán, 2019. "A model-free, non-parametric method for density determination, with application to asset returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 210-221.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:210-221
    DOI: 10.1016/j.physa.2018.11.011
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    References listed on IDEAS

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    1. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-389, July.
    2. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    3. Bartiromo, Rosario, 2013. "Maximum entropy distribution of stock price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1638-1647.
    4. Rosario Bartiromo, 2011. "Maximum entropy distribution of stock price fluctuations," Papers 1106.4957, arXiv.org, revised Oct 2013.
    5. Takaishi, Tetsuya, 2017. "Rational GARCH model: An empirical test for stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 451-460.
    6. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    7. Sornette, Didier, 2001. "Fokker–Planck equation of distributions of financial returns and power laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 290(1), pages 211-217.
    8. D. Sornette & J. V. Andersen & P. Simonetti, 2000. "Portfolio Theory For "Fat Tails"," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 523-535.
    9. Gzyl, Henryk & ter Horst, Enrique & Molina, German, 2015. "A spectral measure estimation problem in rheology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 129-133.
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