Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Kernel estimation of stochastic volatility models

Auteur(s):

Code(s) de Classification MSC:

• 62G05 Estimation
• 62J02 General nonlinear regression

Résumé: In this paper, we study the problem of non parametric estimation of a stochastic volatility model $h_t=\exp(X_t/2)\xi_t, \; X_t=m(X_{t-1}) +\eta_t$ and show that an adaptation of the Kernel estimator proposed by Fan and Truong (1993) estimates the function $m$ with the optimal rate depending on the law of the noise. As those rates vary from powers of $n$ to powers of $\ln(n)$ depending on the characteristic function of the noise, we study the laws for $\xi$ leading to each kind of rates.

Mots Clés: Kernel estimator ; Stochastic volatility model ; Errors-in-variables model

Date: 2000-01-21

Prépublication numéro: PMA-560

Revised version, 2001-01-15 : PMA-560bis.dvi