Nonparametric estimation for a stochastic volatility model

الأصل · EN

Consider discrete time observations (Xℓδ)₁≤ ℓ ≤ ₙ₊₁ of the process X satisfying dXₜ= √Vₜ dBₜ, 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 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.