Structure Database Strategy for Importance Sampling and Application to Pricing Options

Abstract

A framework of combining importance sampling with Structured Database Monte Carlo strategy is developed. The proposed method attempts to devise a generic method for designing importance sampling method. Firstly, evaluation function and objective function are expressed in a way that there is a linear relation between response estimator and majorized function. Order structure is imposed not only on sample paths but also on parameters of candidate density. Then the parameters are estimated by surrogate maximization algorithm. Secondly, cut-off point at which response function can maintain the same sample paths structure is obtained. Based on the low quadratic bound principle and the convexity of the second moment of the estimator, a quadratic surrogate function for objective function is derived. Finally, empirical results show that our approach is straightforward to implement and flexible to be applied in a generic Monte Carlo setting.