Some Further Results on the Tempered Multistable Approach



This article provides new results on the tempered multistable approach. After a preliminary section recalling the main definitions, we show the correspondence between a series representation and a characteristic function representation for asymmetrical field-based tempered multistable processes and for asymmetrical independent increments tempered multistable processes. We also show that both processes are semimartingales, which is a convenient property in finance. Next, we study the structure of autocorrelations that is conveyed by this approach. Finally, we provide an illustration showing the term structures of Value-at-Risk that can be obtained with this model.


Tempered multistable process Non-stationarity Dependence Asymmetry Kurtosis VaR Characteristic function 

Mathematics Subject Classification

60G51 60G52 

JEL Classification




The author wishes to thank Jacques Lévy-Véhel for many fruitful discussions on the topic of the paper and for introducing him to this field of research. The author also thanks Philippe Desurmont, Abdou Kelani, Mohamed Majri, François Quittard-Pinon, Andrea Roncoroni, Hubert Rodarie, Bertrand Tavin, and Christian Walter for their useful comments on the paper, which is the outcome of a collaboration with the SMA Group.


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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.emlyon business schoolEcully CedexFrance

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