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Stochastic volatility : approximation and goodness-of-fit test

Gradinaru M., Nourdin I.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

1--19

Let X be the unique solution started from x0 of the stochastic differential equation dXt= θ(t;Xt)dBt +b(t;Xt)dt with B a standard Brownian motion. We consider an approximation of the volatility θ(t;Xt), 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 convergence as a process. A goodness-of-fit test is also constructed.