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ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES

Published online by Cambridge University Press:  23 June 2008

Feng Gao  and
Fengming Song
Feng Gao*
Affiliation:
Tsinghua University
Fengming Song
Affiliation:
Tsinghua University
*
Address correspondence to Feng Gao, Department of Finance, School of Economics and Management, Tsinghua University, Beijing, P.R. China; e-mail: gaof@sem.tsinghua.edu.cn
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Abstract

Value-at-risk (VaR) and expected shortfall (ES) are now both widely used risk measures. However, users have not paid much attention to the estimation risk issues, especially in the case of heteroskedastic financial time series. The key challenge arises from the fact that the estimated generalized autoregressive conditional heteroskedasticity (GARCH) innovations are not the true independent innovations. The purpose of this work is to provide an analytical method to assess the precision of conditional VaR and ES in the GARCH model estimated by the filtered historical simulation (FHS) method based on the asymptotic behavior of the residual empirical distribution function in GARCH processes. The proposed method is evaluated by simulation and proved valid.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 5 , October 2008 , pp. 1404 - 1424
Copyright
Copyright © Cambridge University Press 2008

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