In this paper, we propose and analyze a novel combination of multilevel
Richardson-Romberg (ML2R) and importance sampling algorithm, with the aim of
reducing the overall computational time, while achieving desired
root-mean-squared error while pricing. We develop an idea to construct the
Monte-Carlo estimator that deals with the parametric change of measure. We rely
on the Robbins-Monro algorithm with projection, in order to approximate optimal
change of measure parameter, for various levels of resolution in our multilevel
algorithm. Furthermore, we propose incorporating discretization schemes with
higher-order strong convergence, in order to simulate the underlying stochastic
differential equations (SDEs) thereby achieving better accuracy. In order to do
so, we study the Central Limit Theorem for the general multilevel algorithm.
Further, we study the asymptotic behavior of our estimator, thereby proving the
Strong Law of Large Numbers. Finally, we present numerical results to
substantiate the efficacy of our developed algorithm