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

In: Risk Assessment

Author

Listed:
  • Sebastian Kring

    (University of Karlsruhe)

  • Svetlozar T. Rachev

    (University of Karlsruhe)

  • Markus Höchstötter

    (University of Karlsruhe)

  • Frank J. Fabozzi

    (Yale School of Management)

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.

Suggested Citation

  • Sebastian Kring & Svetlozar T. Rachev & Markus Höchstötter & Frank J. Fabozzi, 2009. "Estimation of α-Stable Sub-Gaussian Distributions for Asset Returns," Contributions to Economics, in: Georg Bol & Svetlozar T. Rachev & Reinhold Würth (ed.), Risk Assessment, pages 111-152, Springer.
    • Handle: RePEc:spr:conchp:978-3-7908-2050-8_6
    DOI: 10.1007/978-3-7908-2050-8_6
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