Estimation of α-Stable Sub-Gaussian Distributions for Asset Returns

Sebastian Kring (), Svetlozar T. Rachev (), Markus Höchstötter () and Frank J. Fabozzi ()
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Sebastian Kring: University of Karlsruhe
Svetlozar T. Rachev: University of Karlsruhe
Markus Höchstötter: University of Karlsruhe
Frank J. Fabozzi: Yale School of Management

A chapter in Risk Assessment, 2009, pp 111-152 from Springer

Abstract: 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.

Keywords: Random Vector; Asset Return; Stable Distribution; Tail Dependence; Tail Index (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:conchp:978-3-7908-2050-8_6

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DOI: 10.1007/978-3-7908-2050-8_6

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