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The extremal index for GARCH(1,1) processes

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The extremal index for GARCH(1,1) processes. / Laurini, Fabrizio; Tawn, Jonathan Angus.
In: Extremes, Vol. 15, No. 4, 12.2012, p. 511-529.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Laurini, F & Tawn, JA 2012, 'The extremal index for GARCH(1,1) processes', Extremes, vol. 15, no. 4, pp. 511-529.

APA

Laurini, F., & Tawn, J. A. (2012). The extremal index for GARCH(1,1) processes. Extremes, 15(4), 511-529.

Vancouver

Laurini F, Tawn JA. The extremal index for GARCH(1,1) processes. Extremes. 2012 Dec;15(4):511-529. Epub 2012 Mar 8.

Author

Laurini, Fabrizio ; Tawn, Jonathan Angus. / The extremal index for GARCH(1,1) processes. In: Extremes. 2012 ; Vol. 15, No. 4. pp. 511-529.

Bibtex

@article{311785335b4f4f51ba6b4244ea07366e,
title = "The extremal index for GARCH(1,1) processes",
abstract = "Generalised autoregressive conditional heteroskedastic (GARCH) processes have wide application in financial modelling. To characterise the extreme values of this process the extremal index is required. Existing results, which derive the analytical expression for the extremal index for the squared GARCH(1, 1) process, cannot be used to obtain the extremal index for the GARCH(1, 1) process. For the squared GARCH(1, 1) process with symmetric innovations with continuous density function and satisfying a finite moment condition, we derive an alternative analytical expression for the extremal index and new results for the limiting distribution of the size of clusters of extremes. Using these results we obtain an analytical expression for the extremal index of the GARCH(1, 1) process and an algorithm for the evaluation of properties of other cluster functionals and risk measures. We tabulate the extremal index of the GARCH(1, 1) process when the innovations are Student-t and Gaussian distributed.",
keywords = "Clusters, Extreme value theory, External index, Finance, GARCH, Bivariate regular variation",
author = "Fabrizio Laurini and Tawn, {Jonathan Angus}",
year = "2012",
month = dec,
language = "English",
volume = "15",
pages = "511--529",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer Netherlands",
number = "4",

}

RIS

TY - JOUR

T1 - The extremal index for GARCH(1,1) processes

AU - Laurini, Fabrizio

AU - Tawn, Jonathan Angus

PY - 2012/12

Y1 - 2012/12

N2 - Generalised autoregressive conditional heteroskedastic (GARCH) processes have wide application in financial modelling. To characterise the extreme values of this process the extremal index is required. Existing results, which derive the analytical expression for the extremal index for the squared GARCH(1, 1) process, cannot be used to obtain the extremal index for the GARCH(1, 1) process. For the squared GARCH(1, 1) process with symmetric innovations with continuous density function and satisfying a finite moment condition, we derive an alternative analytical expression for the extremal index and new results for the limiting distribution of the size of clusters of extremes. Using these results we obtain an analytical expression for the extremal index of the GARCH(1, 1) process and an algorithm for the evaluation of properties of other cluster functionals and risk measures. We tabulate the extremal index of the GARCH(1, 1) process when the innovations are Student-t and Gaussian distributed.

AB - Generalised autoregressive conditional heteroskedastic (GARCH) processes have wide application in financial modelling. To characterise the extreme values of this process the extremal index is required. Existing results, which derive the analytical expression for the extremal index for the squared GARCH(1, 1) process, cannot be used to obtain the extremal index for the GARCH(1, 1) process. For the squared GARCH(1, 1) process with symmetric innovations with continuous density function and satisfying a finite moment condition, we derive an alternative analytical expression for the extremal index and new results for the limiting distribution of the size of clusters of extremes. Using these results we obtain an analytical expression for the extremal index of the GARCH(1, 1) process and an algorithm for the evaluation of properties of other cluster functionals and risk measures. We tabulate the extremal index of the GARCH(1, 1) process when the innovations are Student-t and Gaussian distributed.

KW - Clusters

KW - Extreme value theory

KW - External index

KW - Finance

KW - GARCH

KW - Bivariate regular variation

M3 - Journal article

VL - 15

SP - 511

EP - 529

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 4

ER -