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Modelling tail risk with tempered stable distributions: an overview

Author

Listed:
  • Hasan Fallahgoul

    (Monash University)

  • Gregoire Loeper

    (Monash University)

Abstract

In this study, we investigate the performance of different parametric models with stable and tempered stable distributions for capturing the tail behaviour of log-returns (financial asset returns). First, we define and discuss the properties of stable and tempered stable random variables. We then show how to estimate their parameters and simulate them based on their characteristic functions. Finally, as an illustration, we conduct an empirical analysis to explore the performance of different models representing the distributions of log-returns for the S&P500 and DAX indexes.

Suggested Citation

  • Hasan Fallahgoul & Gregoire Loeper, 2021. "Modelling tail risk with tempered stable distributions: an overview," Annals of Operations Research, Springer, vol. 299(1), pages 1253-1280, April.
    • Handle: RePEc:spr:annopr:v:299:y:2021:i:1:d:10.1007_s10479-019-03204-3
    DOI: 10.1007/s10479-019-03204-3
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    2. Bianchi, Michele Leonardo & De Luca, Giovanni & Rivieccio, Giorgia, 2023. "Non-Gaussian models for CoVaR estimation," International Journal of Forecasting, Elsevier, vol. 39(1), pages 391-404.

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    More about this item

    Keywords

    Lévy process; Stable distribution; Tail risk; Tempered stable distribution;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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