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Semiparametric estimation of Value at Risk

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Author Info
Jianqing Fan
Juan Gu

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Abstract

Value at Risk (VaR) is a fundamental tool for managing market risks. It measures the worst loss to be expected of a portfolio over a given time horizon under normal market conditions at a given confidence level. Calculation of VaR frequently involves estimating the volatility of return processes and quantiles of standardized returns. In this paper, several semiparametric techniques are introduced to estimate the volatilities of the market prices of a portfolio. In addition, both parametric and nonparametric techniques are proposed to estimate the quantiles of standardized return processes. The newly proposed techniques also have the flexibility to adapt automatically to the changes in the dynamics of market prices over time. Their statistical efficiencies are studied both theoretically and empirically. The combination of newly proposed techniques for estimating volatility and standardized quantiles yields several new techniques for forecasting multiple period VaR. The performance of the newly proposed VaR estimators is evaluated and compared with some of existing methods. Our simulation results and empirical studies endorse the newly proposed time-dependent semiparametric approach for estimating VaR. Copyright Royal Economic Society, 2003

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Publisher Info
Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 6 (2003)
Issue (Month): 2 (December)
Pages: 261-290
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Handle: RePEc:ect:emjrnl:v:6:y:2003:i:2:p:261-290

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  1. Jörg Polzehl & Vladimir Spokoiny, 2006. "Varying coefficient GARCH versus local constant volatility modeling. Comparison of the predictive power," SFB 649 Discussion Papers SFB649DP2006-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Maria Rosa Nieto & Esther Ruiz, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," Statistics and Econometrics Working Papers ws087326, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  3. Marno Verbeek & Jeroen VK Rombouts, 2005. "Evaluating Portfolio Value-at-Risk using Semi-Parametric GARCH Models," Computing in Economics and Finance 2005 40, Society for Computational Economics. [Downloadable!]
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  4. Mstislav Elagin, 2008. "Locally adaptive estimation methods with application to univariate time series," Quantitative Finance Papers 0812.0449, arXiv.org. [Downloadable!]
  5. J. Carlos Escanciano & Jose Olmo, 2007. "Estimation risk effects on backtesting for parametric value-at-risk models," City University Economics Discussion Papers 07/11, Department of Economics, City University, London. [Downloadable!]
  6. Juan Carlos Escanciano & Jose Olmo, 2007. "Backtesting Parametric Value-at-Risk with Estimation Risk," Caepr Working Papers 2007-005_updated, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
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