Logo
Munich Personal RePEc Archive

Risk-parameter estimation in volatility models

Francq, Christian and Zakoian, Jean-Michel (2012): Risk-parameter estimation in volatility models.

[thumbnail of MPRA_paper_41713.pdf]
Preview
PDF
MPRA_paper_41713.pdf

Download (512kB) | Preview

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.

Atom RSS 1.0 RSS 2.0

Contact us: mpra@ub.uni-muenchen.de

This repository has been built using EPrints software.

MPRA is a RePEc service hosted by Logo of the University Library LMU Munich.