Optimal importance sampling in securities pricing

Yi Su and Michael C. Fu

Abstract

ABSTRACT

To reduce variance in estimating security prices via Monte Carlo simulation, we formulate a parametric minimization problem for the optimal importance sampling measure, which is solved using infinitesimal perturbation analysis (IPA) and stochastic approximation (SA). Compared with existing methods, the IPA estimator we derive is more universally applicable and more computationally efficient. Under suitable conditions, we show that the objective function is a convex function, the IPA estimator is unbiased, and the stochastic approximation algorithm converges to the optimum. Lastly, we demonstrate how combining importance sampling with indirect estimation using put–call parity can lead to further substantial variance reduction.