Francq, Christian and Zakoian, JeanMichel (2012): Riskparameter estimation in volatility models.

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Abstract
This paper introduces the concept of risk parameter in conditional volatility models of the form $\epsilon_t=\sigma_t(\theta_0)\eta_t$ and develops statistical procedures to estimate this parameter. For a given risk measure $r$, the risk parameter is expressed as a function of the volatility coefficients $\theta_0$ and the risk, $r(\eta_t)$, of the innovation process. A twostep method is proposed to successively estimate these quantities. An alternative onestep approach, relying on a reparameterization of the model and the use of a non Gaussian QML, is proposed. Asymptotic results are established for smooth risk measures as well as for the ValueatRisk (VaR). Asymptotic comparisons of the two approaches for VaR estimation suggest a superiority of the onestep method when the innovations are heavytailed. For standard GARCH models, the comparison only depends on characteristics of the innovations distribution, not on the volatility parameters. MonteCarlo experiments and an empirical study illustrate these findings.
Item Type:  MPRA Paper 

Original Title:  Riskparameter estimation in volatility models 
Language:  English 
Keywords:  GARCH; Quantile Regression; QuasiMaximum Likelihood; Risk measures; ValueatRisk 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  41713 
Depositing User:  Christian Francq 
Date Deposited:  04. Oct 2012 10:43 
Last Modified:  11. Feb 2013 21:47 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/41713 