Asymptotics for multifactor Volterra type stochastic volatility models

We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti (J. Theor. Probab. 34(2):682-727). We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles.