Nonparametric estimation for a stochastic volatility model

Abstract Consider discrete time observations (X δ)1≤ ≤n+1 of the process X satisfying dXt = √ VtdBt, with Vt 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 their risk. 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. June 23, 2008 Keywords Diffusion coefficient · Drift · Mean square estimator · Model selection · Nonparametric estimation · Penalized contrast · Stochastic volatility Mathematics Subject Classification (2000) 62G08 · 62M05 · 62P05

• Type: Journal
• Year: 2010
• Where: FS
• Authors: F. Comte, V. Genon-Catalot, Yves Rozenholc
• Keywords: Brownian Motion B, Discrete Time Observations, FS 2010, Square Estimator