Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Lévy Processes with Infinite Activities

Abstract: In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for heavy-tailed L\'evy processes, stick-breaking approximation of extrema of L\'evy processes, and the randomized debiasing Monte Carlo scheme. The proposed importance sampling algorithm can be applied to a broad class of L\'evy processes and exhibits significant improvements in efficiency when compared to crude Monte-Carlo method in our numerical experiments.