Estimation of the volatility persistence in a discretly observed diffusion model Mathieu Rosenbaum LS-CREST, Laboratoire de Statistique, Timbre J340, 3 avenue Pierre Larousse, 92240 Malakoff, France. Laboratoire d'Analyse et de Mathematiques Appliquees, CNRS UMR 8050 et Universite de Marne-la-Vallee, France. Abstract We consider the stochastic volatility model dYt = ?t dBt, with B a Brownian motion and ? of the form ?t = ? (∫ t 0 a(u)dWHu ) , where WH is a fractional Brownian motion, independent of the driving Brownian motion B, with Hurst parameter H ≥ 1/2. This model allows for persistence in the volatility ?. The parameter of interest is H and the functions ? and a are treated as nuisance parameters. For a fixed objective time T, we construct from discrete data Yi/n, i = 0, . . . , nT, a wavelet based estimator of H, inspired by adaptive estimation of quadratic functionals. We show that the accuracy of our estimator is n?1/(4H+2) and that this rate is optimal in a minimax sense. Resume On considere le modele a volatilite stochastique defini par les equations precedentes, ou B est un mouvement brownien et WH un mouvement brownien fractionnaire, independant de B, de parametre de Hurst H ≥ 1/2.
- fractional brownian
- stochastic volatility
- stochastique defini par les equations precedentes
- proprietes de persistance dans la volatilite ?
- rate vn
- objective time