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

Henryk Gzyl (), Enrique ter Horst and Germán Molina

Physica A: Statistical Mechanics and its Applications, 2019, vol. 517, issue C, 210-221

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.

Keywords: Density estimation; Returns; Percent error; Laplace transform; Maximum entropy; Fractional moments (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:517:y:2019:i:c:p:210-221

DOI: 10.1016/j.physa.2018.11.011

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