Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model Using Malliavin Integration by Parts

In this article, we establish an integration by parts formula for the quadrature of discontinuous payoffs in a multidimensional Heston model. For its derivation we use Malliavin calculus techniques and work under mild integrability conditions on the payoff and under the assumption of a strictly positive volatility. The integration by parts procedure smoothes the original functional, and thus our formula in combination with a payoff splitting allows us to construct efficient multilevel Monte Carlo estimators. This is confirmed by our numerical analysis and is illustrated by several numerical examples.