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On Accelerating Monte Carlo Integration Using Orthogonal Projections

Author

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  • Huei-Wen Teng

    (National Yang Ming Chiao Tung University)

  • Ming-Hsuan Kang

    (National Yang Ming Chiao Tung University)

Abstract

Monte Carlo simulation is an indispensable tool in calculating high-dimensional integrals. Although Monte Carlo integration is notoriously known for its slow convergence, it could be improved by various variance reduction techniques. This paper applies orthogonal projections to study the amount of variance reduction, and also proposes a novel projection estimator that is associated with a group of symmetries of the probability measure. For a given space of functions, the average variance reduction can be derived. For a specific function, its variance reduction is also analyzed. The well-known antithetic estimator is a special case of the projection estimator, and new results of its variance reduction and efficiency are provided. Various illustrations including pricing financial Asian options are provided to confirm our claims.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09893-3
    DOI: 10.1007/s11009-021-09893-3
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    References listed on IDEAS

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    1. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    2. Jong Jun Park & Geon Ho Choe, 2016. "A new variance reduction method for option pricing based on sampling the vertices of a simplex," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1165-1173, August.
    3. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
    4. Jan Neddermeyer, 2011. "Non-parametric partial importance sampling for financial derivative pricing," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1193-1206.
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