Nonparametric estimation for a stochastic volatility model

Fabienne Comte; Valentine Genon-Catalot; Yves Rozenholc

paper

Nonparametric estimation for a stochastic volatility model

arXiv:0712.3735

Abstract

Consider discrete time observations (X_{\ellδ})_{1\leq \ell \leq n+1} $o f t h e p r ocess$ X $s a t i s f y in g$ dX_t= \sqrt{V_t} dB_t $, w i t h$ V_t $a o n e - d im e n s i o na l p os i t i v e d i f f u s i o n p r ocess in d e p e n d e n t o f t h e B r o w nianm o t i o n$ B $. F or b o t h t h e d r i f t an d t h e d i f f u s i o n coe f f i c i e n t o f t h e u n o b ser v e dd i f f u s i o n$ 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.