Least Squares Importance Sampling for Monte Carlo Security Pricing

Details Least Squares Importance Sampling for Monte Carlo Security Pricing Least Squares Importance Sampling for Monte Carlo Security Pricing

2007-03-18

arxiv.org/abs/physics/0703181v1

Physics

Physics and Society

12 pages, 4 figures

Scientific paper

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, when the latter are known to perform well. However, in contrast to traditional approaches, LSIS is not limited to the determination of the optimal mean of a Gaussian sampling distribution. As a result, it outperforms other methods 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.

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