Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models |
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Authors: | Andreas Behr Ulrich Pötter |
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Institution: | 1. Institute for Econometrics, University of Münster, Am Stadtgraben 9, 48143, Münster, Germany 2. Faculty of Social Science, University of Bochum, Universit?tsstrasse 150, 44801, Bochum, Germany
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Abstract: | Simple parametric models of the marginal distribution of stock returns are an essential building block in many areas of applied
finance. Even though it is well known that the normal distribution fails to represent most of the “stylised” facts characterising
return distributions, it still dominates much of the applied work in finance. Using monthly S&P 500 stock index returns (1871–2005)
as well as daily returns (2001–2005), we investigate the viability of three alternative parametric families to represent both
the stylised and empirical facts: the generalised hyperbolic distribution, the generalised logF distribution, and finite mixtures
of Gaussians. For monthly return data, all three alternatives give reasonable fits for all sub-periods. However, the generalised
hyperbolic distribution fails to describe some features of the marginal distributions in some sub-periods. The daily return
data are much more symmetric and expose another problem for all three distributions: the parameters describing the behaviour
of the tails also influence the scale so that simpler alternatives or restricted parameterisations are called for.
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Keywords: | Stock returns Non-normality Gaussian mixtures Generalised hyperbolic distribution Generalised logF distribution |
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