Nonparametric estimation for a stochastic volatility model.

Fabienne Comte (1) , Valentine Genon-Catalot (1) , Yves Rozenholc (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the drift and the diffusion coefficient of the unobserved diffusion $V$, we propose nonparametric least square estimators, and provide bounds for theirrisk. Estimators are chosen among a collection of functions belonging to a finite dimensional space whose dimension is selected by a data driven procedure. Implementation on simulated data illustrates how the method works.

Mots clés: Diffusion coefficient; Drift; Mean square estimator; Model selection; Nonparametric estimation; Penalized contrast; Stochastic volatility

Domaines: Méthodologie [stat.ME]; Statistiques [math.ST]; Théorie [stat.TH]

Fabienne Comte, Valentine Genon-Catalot, Yves Rozenholc. Nonparametric estimation for a stochastic volatility model.. Finance and Stochastics, 2010, 14 (1), pp.49-80. ⟨10.1007/s00780-009-0094-z⟩. ⟨hal-00200874⟩