Importance Sampling in Derivative Securities Pricing

We formulate the importance sampling problem as a parametric minimization problem under the original measure and use a combination of infinitesimal perturbation analysis (IPA) and stochastic approximation (SA) to minimize the variance of the price estimation. Compared to existing methods, the IPA estimator derived in this paper has significantly smaller estimation variance and doesn’t depend on the form of payoff functions and differentiability of the sample path, and thus is more universally applicable and computationally efficient. Under suitable conditions, the objective function is a convex function, the IPA estimator presented is unbiased, and the corresponding stochastic approximation algorithm converges to the true optimal value.