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Adaptive Optimal Allocation in Stratified Sampling Methods

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  • Pierre Étoré

    (LJK)

  • Benjamin Jourdain

    (Université Paris-Est)

Abstract

In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These proportions converge to the optimal allocation in terms of variance reduction and our stratified estimator is asymptotically normal with asymptotic variance equal to the minimal one. Numerical experiments confirm the efficiency of our algorithm. For the pricing of arithmetic average Asian options in the Black and Scholes model, the variance is divided by a factor going from 1.1 to 50.4 (depending on the option type and the moneyness) in comparison with the standard allocation procedure, while the increase in computation time does not overcome 1%.

Suggested Citation

  • Pierre Étoré & Benjamin Jourdain, 2010. "Adaptive Optimal Allocation in Stratified Sampling Methods," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 335-360, September.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9108-0
    DOI: 10.1007/s11009-008-9108-0
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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.
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    Cited by:

    1. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2013. "Control variates and conditional Monte Carlo for basket and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 421-434.
    2. Corlay Sylvain & Pagès Gilles, 2015. "Functional quantization-based stratified sampling methods," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 1-32, March.
    3. Sak, Halis & Başoğlu, İsmail, 2017. "Efficient randomized quasi-Monte Carlo methods for portfolio market risk," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 87-94.
    4. Sayah, Toni, 2019. "Adaptive stratified Monte Carlo algorithm for numerical computation of integrals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 143-158.
    5. Kamlesh Kumar Pandey & Diwakar Shukla, 2022. "Stratified linear systematic sampling based clustering approach for detection of financial risk group by mining of big data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(3), pages 1239-1253, June.

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