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pTAS distributions with application to risk management

Author

Listed:
  • Matthias Fischer

    (FAU Erlangen-Nürnberg)

  • Kevin Jakob

    (University of Augsburg)

Abstract

The family of positive tempered α-stable (pTAS) or sometimes also tempered one-sided α-stable distributions dates back to Tweedie (1984) and Hougaard (1986) who discussed it in the context of frailty distribution in life table methods for heterogenous populations. The pTAS family generalizes the well-known gamma distribution and allows for heavier tails depending on the parameter α. Because of this property, pTAS distributions appear to be useful in the context of risk management. Against this background, the contribution of his work is three-fold: Firstly, we summarize the properties of the pTAS family. Secondly, we describe its numerical implementation and illustrate the functions by means of R examples in the Appendix. Thirdly, we empirically demonstrate that this family can be successfully applied in risk management. Concretely, applications to credit and operational risk are given.

Suggested Citation

  • Matthias Fischer & Kevin Jakob, 2016. "pTAS distributions with application to risk management," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-18, December.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0049-9
    DOI: 10.1186/s40488-016-0049-9
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    References listed on IDEAS

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    1. Neil Shephard & Ole E. Barndorff-Nielsen & University of Aarhus, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 72, University of Oxford, Department of Economics.
    2. Karen J. Palmer & Martin S. Ridout & Byron J. T. Morgan, 2008. "Modelling cell generation times by using the tempered stable distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 379-397, September.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. Cheng-Few Lee & John C. Lee (ed.), 2015. "Handbook of Financial Econometrics and Statistics," Springer Books, Springer, edition 127, number 978-1-4614-7750-1, October.
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