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Consistent Estimation of the Value-at-Risk when the Error Distribution of the Volatility Model is Misspecified
Year Of Publication: 2013
Month Of Publication: October
Resource Link: Click here to open
Pages: 38
Download Count: 0
View Count: 1366
Comment Num: 0
Language: English
Source: working paper
Who Can Read: Free
Date: 11-10-2013
Publisher: Administrator
Summary
A two-step approach for conditional Value at Risk (VaR) estimation is considered. In the first step, a generalized-quasi-maximum likelihood estimator (gQMLE) is employed to estimate the volatility parameter, and in the second step the empirical quantile of the residuals serves to estimate the theoretical quantile of the innovations. When the instrumental density of the gQMLE is not the Gaussian density utilized in the standard QMLE, or is not the true distribution of the innovations, both the estimations of the volatility and of the quantile are asymptotically biased. The two errors however counterbalance each other, and we finally obtain a consistent estimator of the conditional VaR. For a wide class of GARCH models, we derive the asymptotic distribution of the VaR estimation based on gQMLE. We show that the optimal instrumental density depends neither on the GARCH parameter nor on the risk level, but only on the distribution of the innovations.
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Author(s)
el Ghourabi, Mohamed Sign in to follow this author
Francq, C_hristian Sign in to follow this author
Telmoudi, Fedya Sign in to follow this author
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