https://hal-upec-upem.archives-ouvertes.fr/hal-00693752Genon-Catalot, VVGenon-CatalotLAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - Fédération de Recherche Bézout - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche ScientifiqueJeantheau, TTJeantheauLaredo, CCLaredoStochastic volatility models as hidden Markov models and statistical applicationsHAL CCSD2000[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Lama, Admin2012-05-02 23:18:292022-01-15 04:13:012012-05-02 23:18:34enJournal articles10.2307/33184711This paper deals with the fixed sampling interval case for stochastic volatility models. We consider a two-dimensional diffusion process (Y-t, V-t), where only (Y-t) is observed at n discrete times with regular sampling interval Delta. The unobserved coordinate (V-t) is ergodic and rules the diffusion coefficient (volatility) of (Y-t). We study the ergodicity and mixing properties of the observations (Y-i Delta). For this purpose, we first present a thorough review of these properties for stationary diffusions. We then prove that our observations can be viewed as a hidden Markov model and inherit the mixing properties of (V-t). When the stochastic differential equation of (V-t) depends on unknown parameters, we derive moment-type estimators of all the parameters, and show almost sure convergence and a central limit theorem at rate n(1/2). Examples of models coming from finance are fully treated. We focus on the asymptotic variances of the estimators and establish some links with the small sampling interval case studied in previous papers.