Importance sampling for jump processes and applications to finance

Abstract: Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the standard exponential tilting for the Brownian motion. The free parameters of our framework are optimized using sample average approximation techniques. We illustrate the efficiency of our method on the valuation of financial derivatives in several jump models.