Estimation Adjusted VaR
AbstractStandard risk measures, such as the Value-at-Risk (VaR), or the Expected Shortfall, have to be estimated and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the Profit and Loss variable, induces an asymptotic bias of order 1/n in the coverage probabilities. This paper shows how to correct for this bias by introducing a new estimator of the VaR, called Estimation adjusted VaR (EVaR). This adjustment allows for a joint treatment of theoretical and estimation risks, taking into account for their possible dependence. The estimator is derived for a general parametric dynamic model and is particularized to stochastic drift and volatility models. The finite sample properties of the EVaR estimator are studied by simulation and an empirical study of the S&P Index is proposed
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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2012-16.
Date of creation: Sep 2012
Date of revision:
Value-at-Risk; Estimation Risk; Bias Correction; ARCH Model;
Other versions of this item:
- NEP-ALL-2012-10-06 (All new papers)
- NEP-BAN-2012-10-06 (Banking)
- NEP-ECM-2012-10-06 (Econometrics)
- NEP-RMG-2012-10-06 (Risk Management)
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