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Non-parametric partial importance sampling for financial derivative pricing

Author

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  • Jan Neddermeyer

Abstract

Importance sampling is a promising variance reduction technique for Monte Carlo simulation-based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm that estimates the optimal proposal non-parametrically using a multivariate frequency polygon estimator. In contrast to parametric methods, non-parametric estimation allows for close approximation of the optimal proposal. Standard non-parametric importance sampling is inefficient for high-dimensional problems. We solve this issue by applying the procedure to a low-dimensional subspace, which is identified through principal component analysis and the concept of the effective dimension. The mean square error properties of the algorithm are investigated and its asymptotic optimality is shown. Quasi-Monte Carlo is used for further improvement of the method. It is easy to implement, particularly it does not require any analytical computation, and it is computationally very efficient. We demonstrate through path-dependent and multi-asset option pricing problems that the algorithm leads to significant efficiency gains compared with other algorithms in the literature.

Suggested Citation

  • Jan Neddermeyer, 2011. "Non-parametric partial importance sampling for financial derivative pricing," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1193-1206.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:8:p:1193-1206
    DOI: 10.1080/14697680903496485
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    Citations

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    Cited by:

    1. Erik Hintz & Marius Hofert & Christiane Lemieux & Yoshihiro Taniguchi, 2022. "Single-Index Importance Sampling with Stratification," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3049-3073, December.
    2. 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.
    3. Huei-Wen Teng & Ming-Hsuan Kang, 2022. "On Accelerating Monte Carlo Integration Using Orthogonal Projections," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1143-1168, June.
    4. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.

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