On sample average approximation algorithms for determining the optimal importance sampling parameters in pricing financial derivatives on Lévy processes

We formulate the problem of determining the optimal importance sampling measure change for pricing financial derivatives under Lévy processes as a parametric optimization problem, and propose a solution approach using sample average approximation (SAA) with Newton iteration to find the optimal parameters in the Esscher probability measure change. Theoretical results, such as convergence rate of the optimal solutions, are provided. A numerical example illustrates the effectiveness of the approach.