Estimation of α-stable sub-Gaussian distributions for asset returns

Sebastian Kring, Svetlozar T. Rachev, Markus Höchstötter, Frank J. Fabozzi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

20 Scopus citations


Fitting multivariate α-stable distributions to data is still not feasible in higher dimensions since the (non-parametric) spectral measure of the characteristic function is extremely difficult to estimate in dimensions higher than 2. This was shown by [3] and [15]. α-stable sub-Gaussian distributions are a particular (parametric) subclass of the multivariate α-stable distributions. We present and extend a method based on [16] to estimate the dispersion matrix of an α-stable sub-Gaussian distribution and estimate the tail index α of the dis-tribution. In particular, we develop an estimator for the off-diagonal entries of the dispersion matrix that has statistical properties superior to the normal off-diagonal estimator based on the covariation. Furthermore, this approach allows estimation of the dispersion matrix of any normal variance mixture distribution up to a scale parameter. We demonstrate the behaviour of these estimators by fitting an α-stable sub-Gaussian distribution to the DAX30 components. Finally, we conduct a stable principal component analysis and calculate the coefficient of tail dependence of the prinipal components.

Original languageEnglish
Title of host publicationRisk Assessment
Subtitle of host publicationDecisions in Banking and Finance
EditorsGeorg Bol, Svetlozar Rachev, Reinhold Wurth
Number of pages42
StatePublished - 2009

Publication series

NameContributions to Economics
ISSN (Print)1431-1933


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