Stochastic volatility: approximation and goodness-of-fit test

Mihai Gradinaru (1, 2) , Ivan Nourdin (1, 3)

1 IECN - Institut Élie Cartan de Nancy
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Let $X$ be the unique solution started from $x_0$ of the stochastic differential equation $dX_t=\theta(t,X_t)dB_t+b(t,X_t)dt$, with $B$ a standard Brownian motion. We consider an approximation of the volatility $\theta(t,X_t)$, the drift being considered as a nuisance parameter. The approximation is based on a discrete time observation of $X$ and we study its rate of the convergence as a process. A goodness-of-fit test is also constructed.

Mots clés: non-parametric estimation; goodness-of-fit test; stochastic volatility; discrete time observation

Domaines: Probabilités [math.PR]; Théorie [stat.TH]; Statistiques [math.ST]

Mihai Gradinaru, Ivan Nourdin. Stochastic volatility: approximation and goodness-of-fit test. Probability and Mathematical Statistics, 2008, 28 (1), pp.1-19. ⟨hal-00150761⟩