  We consider a multidimensional It\^o process $Y=(Y_t)_{t\in[0,T]}$ with some
unknown drift coefficient process $b_t$ and volatility coefficient
$\sigma(X_t,\theta)$ with covariate process $X=(X_t)_{t\in[0,T]}$, the function
$\sigma(x,\theta)$ being known up to $\theta\in\Theta$. For this model we
consider a change point problem for the parameter $\theta$ in the volatility
component. The change is supposed to occur at some point $t^*\in (0,T)$. Given
discrete time observations from the process $(X,Y)$, we propose quasi-maximum
likelihood estimation of the change point. We present the rate of convergence
of the change point estimator and the limit thereoms of aymptotically mixed
type.
