Approximating Volatility Diffusions with Cev-Arch Models

41 Pages Posted: 29 Jan 2004

See all articles by Fabio Fornari

Fabio Fornari

European Central Bank (ECB)

Antonio Mele

University of Lugano; Swiss Finance Institute; Centre for Economic Policy Research (CEPR)

Date Written: January 15, 2004


Aim of this article is to judge the empirical performance of Arch as diffusion approximations to models of the short-term rate with stochastic volatility and as filters of the unobserved volatility. We show that the estimation of the continuous time scheme to which a discrete time Arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time coefficients. A natural substitute of a global specification test for just-identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias. Unlike previous literature in which standard Arch models approximated only specific diffusions, our estimation strategy relies on a new Arch model that approximates any CEV-diffusion model for the conditional volatility. A Monte-Carlo study reveals that the filtering performances of this model are remarkably good, even in the presence of an important kind of misspecification.

Keywords: Stochastic volatility, Arch filtering, indirect inference

JEL Classification: C15, E43, G12

Suggested Citation

Fornari, Fabio and Mele, Antonio, Approximating Volatility Diffusions with Cev-Arch Models (January 15, 2004). Available at SSRN: or

Fabio Fornari (Contact Author)

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314

Antonio Mele

University of Lugano ( email )

Via Buffi 13
Lugano, 6900


Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

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