| Stochastic volatility: approximation and goodness-of-fit test (2008) | |||||||||||||||
Abstract | |||||||||||||||
| 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. | |||||||||||||||
Publication details | |||||||||||||||
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