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Document type:
Zeitschriftenaufsatz 
Author(s):
Klüppelberg, C. and Zhang, J. 
Title:
Time-consistency of risk measures with GARCH volatilities and their estimation 
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:
Pages contribution:
103-124 
Reviewed:
ja 
Language:
en 
Fulltext / DOI:
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