Before revision:  Since one limitation of hybrid models is the unavailability of analytical pricing formula  of variance swaps  due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
After revision:  This full correlation structure possess the limitation to have fully analytical pricing formula of variance swaps due to the non-affinity property , we obtain an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.