  We prove a large deviations principle for the class of multidimensional
affine stochastic volatility models considered in (Gourieroux, C. and Sufana,
R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled
by a Wishart process. This class extends the very popular Heston model to the
multivariate setting, thus allowing to model the joint behaviour of a basket of
stocks or several interest rates. We then use the large deviation principle to
obtain an asymptotic approximation for the implied volatility of basket options
and to develop an asymptotically optimal importance sampling algorithm, to
reduce the number of simulations when using Monte-Carlo methods to price
derivatives.
