Affordable Access

Publisher Website

Reconsidering the continuous time limit of the GARCH(1, 1) process

Authors
Journal
Journal of Econometrics
0304-4076
Publisher
Elsevier
Publication Date
Volume
96
Issue
1
Identifiers
DOI: 10.1016/s0304-4076(99)00053-6
Keywords
  • Degenerate Diffusions
  • Diffusion Approximation
  • Garch
Disciplines
  • Mathematics

Abstract

Abstract In this note we reconsider the continuous time limit of the GARCH(1, 1) process. Let Y k and σ k 2 denote, respectively, the cumulative returns and the volatility processes. We consider the continuous time approximation of the couple (Y k, σ k 2). We show that, by choosing different parameterizations, as a function of the discrete interval h, we can obtain either a degenerate or a non-degenerate diffusion limit. We then show that GARCH(1, 1) processes can be obtained as Euler approximations of degenerate diffusions, while any Euler approximation of a non-degenerate diffusion is a stochastic volatility process.

There are no comments yet on this publication. Be the first to share your thoughts.