Polynomial programming approach to weak approximation of Lévy-driven stochastic differential equations with application to option pricing

We propose an optimization approach to weak approximation of Levy-driven stochastic differential equations. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target expectation, where the optimization procedure ends up with a polynomial programming problem. An advantage of our approach is that all we need is a closed form of the Levy measure, not the exact simulation knowledge of the increments or of a shot noise representation for the time discretization approximation. We present numerical examples of the computation of the moments, as well as the European call option premium, of the Doléans-Dade exponential model.