Computing Greeks with Multilevel Monte Carlo Methods using Importance Sampling

This paper presents a new efficient way to reduce the variance of an estimator of popular payoffs and greeks encounter in financial mathematics. The idea is to apply Importance Sampling with the Multilevel Monte Carlo recently introduced by M.B. Giles. So far, Importance Sampling was proved successful in combination with standard Monte Carlo method. We will show efficiency of our approach on the estimation of financial derivatives prices and then on the estimation of Greeks (i.e. sensitivities of the payoffs with regards to the model parameters). We will perform our analysis in the Black & Scholes’ framework. This study is then aimed to experiment and compare the impact of Importance Sampling on Multilevel Monte Carlo variance