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Least-squares Importance Sampling for Monte Carlo security pricing

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  • Luca Capriotti

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.

Suggested Citation

  • Luca Capriotti, 2008. "Least-squares Importance Sampling for Monte Carlo security pricing," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 485-497.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:5:p:485-497
    DOI: 10.1080/14697680701762435
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    References listed on IDEAS

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    1. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, October.
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    Cited by:

    1. Huei-Wen Teng & Cheng-Der Fuh & Chun-Chieh Chen, 2016. "On an automatic and optimal importance sampling approach with applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1259-1271, August.
    2. Alexander, Carol & Meng, Xiaochun & Wei, Wei, 2022. "Targeting Kollo skewness with random orthogonal matrix simulation," European Journal of Operational Research, Elsevier, vol. 299(1), pages 362-376.
    3. Carol Alexander & Xiaochun Meng & Wei Wei, 2020. "Targetting Kollo Skewness with Random Orthogonal Matrix Simulation," Papers 2004.06586, arXiv.org, revised Sep 2021.

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