We develop a variance reduction technique, based on importance sampling in con- junction with the stochastic Robbins–Monro algorithm, for option prices of jump– diffusion models with stochastic volatility. This is done by combining the work developed by Arouna for pricing diffusion  models, and extended by Kawai for Lévy processes without a Brownian  component. We apply this technique to improve the numerical computation of derivative price sensitivities for general Lévy processes, allowing  both Brownian  and jump parts. Numerical  examples are performed for both the Black–Scholes and Heston models with jumps and for the Barndorff–Nielsen–Shephard model to illustrate the efficiency  of this numerical technique. The numerical results support that the proposed methodology improves the efficiency of the usual Monte Carlo procedures.