Least-squares Importance Sampling for Monte Carlo security pricing

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least-squares optimization procedure. With several numerical examples, we show that such Least-squares Importance Sampling (LSIS) provides efficiency gains comparable to the state-of-the-art techniques, for problems that can be formulated in terms of the determination of the optimal mean of a multivariate Gaussian distribution. In addition, LSIS can be naturally applied to more general Importance Sampling densities and is particularly effective when the ability to adjust higher moments of the sampling distribution, or to deal with non-Gaussian or multi-modal densities, is critical to achieve variance reductions.