A link between complete models with stochastic volatility and ARCH models
type: Item
instance of: scholarly article
title: A link between complete models with stochastic volatility and ARCH models
zbMATH Open document ID: 1098.91052
author: Thierry Jeantheau
published in: Finance and Stochastics
publication date: 2004-11-24T00:00:00Z
review text: The author proposes a heteroscedastic model in discrete time which converges, when the sampling interval goes to zero, towards the special complete model with stochastic volatility in continuous time. The aim of the paper is to investigate the link between ARCH models and the complete model with stochastic volatility of \textit{David G. Hobson} and \textit{L. C. G. Rogers} [Math. Finance 8, No. 1, 27--48 (1998; Zbl 0908.90012)]. Under a simple assumption on the rate of convergence of the parameters, the discrete-time model, which is conditionally heteroscedastic, converges to the diffusion process, that is a complete model with stochastic volatility. This diffusion approximation result provides a numerical scheme, to approximate the Hobson and Rogers model. The stationary and moment properties of the model are studied. The consistency of the pseudo conditional likelihood maximum estimates for this specific model are proved.
Mathematics Subject Classification ID: 91G70
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 2118691
zbMATH Keywords: ARCH models
zbMATH Keywords: stochastic volatility
zbMATH Keywords: diffusion approximation
zbMATH Keywords: Markov chain
zbMATH Keywords: asymptotic theory
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s00780-003-0103-6
OpenAlex ID: W2084698072
DOI: 10.1007/S00780-003-0103-6
description: scientific article; zbMATH DE number 2118691