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A tail quantile approximation formula for the student t and the symmetric generalized hyperbolic distribution

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  • Schlüter, Stephan
  • Fischer, Matthias J.

Abstract

Calculating a large number of tail probabilities or tail quantiles for a given distribution families becomes very challenging, if both the cumulative and the inverse distribution function are not available in closed form. In case of the Gaussian and Student t distribution, quantile approximations are already available. This is not the case for the (symmetric) generalized hyperbolic distribution (GHD) whose popularity steadily increases and which includes both Gaussian and Student t as limiting case. Within this paper we close this gap and derive one possible tail approximation formula for the GHD as well as for the Student t distribution.

Suggested Citation

  • Schlüter, Stephan & Fischer, Matthias J., 2009. "A tail quantile approximation formula for the student t and the symmetric generalized hyperbolic distribution," FAU Discussion Papers in Economics 05/2009, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
  • Handle: RePEc:zbw:iwqwdp:052009
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    Keywords

    Generalized hyperbolic distribution; Quantile approximation; Student t distribution;

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