Risk-parameter estimation in volatility models

Christian Francq and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

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 two-step method is proposed to successively estimate these quantities. An alternative one-step 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 Value-at-Risk (VaR). Asymptotic comparisons of the two approaches for VaR estimation suggest a superiority of the one-step method when the innovations are heavy-tailed. For standard GARCH models, the comparison only depends on characteristics of the innovations distribution, not on the volatility parameters. Monte-Carlo experiments and an empirical study illustrate these findings.

Keywords: GARCH; Quantile Regression; Quasi-Maximum Likelihood; Risk measures; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2012-10-04
New Economics Papers: this item is included in nep-ecm and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Journal Article: Risk-parameter estimation in volatility models (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:41713

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