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Least Squares Importance Sampling for Monte Carlo Security Pricing

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Capriotti, Luca

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Abstract 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.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method theory application
Free Keywords Monte Carlo methods; Derivatives pricing; Financial derivatives; Financial engineering
Publication Year 2008
Page/Pages p. 485-497
Journal Quantitative Finance, 8 (2008) 5
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)