Extremes of supOU Processes

Vicky Fasen; Claudia Klüppelberg

doi:10.1007/978-3-540-70847-6_14

Extremes of supOU Processes

Vicky Fasen, Claudia Klüppelberg

Chair of Mathematical Statistics

Technical University of Munich

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

29 Scopus citations

Abstract

Barndorff-Nielsen and Shephard [3] investigate supOU processes as volatility models. Empirical volatility has tails heavier than normal, long memory in the sense that the empirical autocorrelation function decreases slower than exponential, and exhibits volatility clusters on high levels. We investigate supOU processes with respect to these stylized facts. The class of supOU processes is vast and can be distinguished by its underlying driving Levy process. Within the class of convolution equivalent distributions we shall show that extremal clusters and long range dependence only occur for supOU processes, whose underlying driving Levy process has regularly varying increments. The results on the extremal behavior of supOU processes correspond to the results of classical Lévy-driven OU processes.

Original language	English
Title of host publication	Stochastic Analysis and Applications
Subtitle of host publication	The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito
Publisher	Springer Verlag
Pages	339-359
Number of pages	21
ISBN (Print)	3540708464, 9783540708469
DOIs	https://doi.org/10.1007/978-3-540-70847-6_14
State	Published - 2007
Event	2nd Abel Symposium 2005: Stochastic Analysis and Applications - Oslo, Norway Duration: 29 Jul 2005 → 4 Aug 2005

Publication series

Name	Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito

Conference

Conference	2nd Abel Symposium 2005: Stochastic Analysis and Applications
Country/Territory	Norway
City	Oslo
Period	29/07/05 → 4/08/05

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10.1007/978-3-540-70847-6_14

Cite this

Fasen, V., & Klüppelberg, C. (2007). Extremes of supOU Processes. In Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito (pp. 339-359). (Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito). Springer Verlag. https://doi.org/10.1007/978-3-540-70847-6_14

Fasen, Vicky ; Klüppelberg, Claudia. / Extremes of supOU Processes. Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito. Springer Verlag, 2007. pp. 339-359 (Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito).

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title = "Extremes of supOU Processes",

abstract = "Barndorff-Nielsen and Shephard [3] investigate supOU processes as volatility models. Empirical volatility has tails heavier than normal, long memory in the sense that the empirical autocorrelation function decreases slower than exponential, and exhibits volatility clusters on high levels. We investigate supOU processes with respect to these stylized facts. The class of supOU processes is vast and can be distinguished by its underlying driving Levy process. Within the class of convolution equivalent distributions we shall show that extremal clusters and long range dependence only occur for supOU processes, whose underlying driving Levy process has regularly varying increments. The results on the extremal behavior of supOU processes correspond to the results of classical L{\'e}vy-driven OU processes.",

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Fasen, V & Klüppelberg, C 2007, Extremes of supOU Processes. in Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito. Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito, Springer Verlag, pp. 339-359, 2nd Abel Symposium 2005: Stochastic Analysis and Applications, Oslo, Norway, 29/07/05. https://doi.org/10.1007/978-3-540-70847-6_14

Extremes of supOU Processes. / Fasen, Vicky; Klüppelberg, Claudia.
Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito. Springer Verlag, 2007. p. 339-359 (Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Barndorff-Nielsen and Shephard [3] investigate supOU processes as volatility models. Empirical volatility has tails heavier than normal, long memory in the sense that the empirical autocorrelation function decreases slower than exponential, and exhibits volatility clusters on high levels. We investigate supOU processes with respect to these stylized facts. The class of supOU processes is vast and can be distinguished by its underlying driving Levy process. Within the class of convolution equivalent distributions we shall show that extremal clusters and long range dependence only occur for supOU processes, whose underlying driving Levy process has regularly varying increments. The results on the extremal behavior of supOU processes correspond to the results of classical Lévy-driven OU processes.

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Fasen V, Klüppelberg C. Extremes of supOU Processes. In Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito. Springer Verlag. 2007. p. 339-359. (Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito). doi: 10.1007/978-3-540-70847-6_14

Extremes of supOU Processes

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