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Title:

Time-consistency of risk measures with GARCH volatilities and their estimation

Document type:
Zeitschriftenaufsatz
Author(s):
Klüppelberg, C. and Zhang, J.
Abstract:
In this paper we study time-consistent risk measures for returns that are given by a GARCH (1; 1) model. We present a construction of risk measures based on their static counterparts that over-comes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average Value-at-Risk (AVaR). While in the VaR case we can derive an analytical formula for its time-consistent counterpart, in the AVaR case we derive lower and upper bounds to its ti...     »
Keywords:
dynamic risk measure, time-consistency, GARCH ( 1 ; 1 ) , Extreme Value Theory, Value-at-Risk, Average Value-at-Risk, Expected Shortfall, Generalized Pareto distribution, aggregate returns
Dewey Decimal Classification:
510 Mathematik
Journal title:
Statistics & Risk Modeling
Year:
2016
Journal volume:
32
Year / month:
2016-03
Quarter:
1. Quartal
Month:
Mar
Journal issue:
2
Pages contribution:
103-124
Reviewed:
ja
Language:
en
Fulltext / DOI:
doi:10.1515/strm-2015-0010
WWW:
Statistics & Risk Modeling
Publisher:
De Gruyter
Publisher address:
Berlin
Print-ISSN:
2193-1402
E-ISSN:
2196-7040
Notes:
Online erschienen: 24.02.2016
Status:
Verlagsversion / published
Accepted:
08.02.2016
Date of publication:
01.03.2016
Semester:
WS 15-16
TUM Institution:
Lehrstuhl für Mathematische Statistik
Format:
Text
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