IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v12y2010i3d10.1007_s11009-008-9108-0.html
   My bibliography  Save this article

Adaptive Optimal Allocation in Stratified Sampling Methods

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-008-9108-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11009-008-9108-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han, Chulwoo & Park, Frank C., 2022. "A geometric framework for covariance dynamics," Journal of Banking & Finance, Elsevier, vol. 134(C).
    2. Xueping Wu & Jin Zhang, 1999. "Options on the minimum or the maximum of two average prices," Review of Derivatives Research, Springer, vol. 3(2), pages 183-204, May.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    4. Shih-Kuei Lin & Ren-Her Wang & Cheng-Der Fuh, 2006. "Risk Management for Linear and Non-Linear Assets: A Bootstrap Method with Importance Resampling to Evaluate Value-at-Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(3), pages 261-295, September.
    5. Genin, Adrien & Tankov, Peter, 2020. "Optimal importance sampling for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 20-46.
    6. Ma, Xiaocui & Xi, Fubao, 2017. "Moderate deviations for neutral stochastic differential delay equations with jumps," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 97-107.
    7. Xiaoqun Wang & Ian H. Sloan, 2011. "Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction," Operations Research, INFORMS, vol. 59(1), pages 80-95, February.
    8. Pierre Etore & Gersende Fort & Benjamin Jourdain & Eric Moulines, 2011. "On adaptive stratification," Annals of Operations Research, Springer, vol. 189(1), pages 127-154, September.
    9. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    10. 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.
    11. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    12. 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.
    13. Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
    14. Frikha Noufel & Sagna Abass, 2012. "Quantization based recursive importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 287-326, December.
    15. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    16. Kahalé, Nabil, 2020. "General multilevel Monte Carlo methods for pricing discretely monitored Asian options," European Journal of Operational Research, Elsevier, vol. 287(2), pages 739-748.
    17. Arouna Bouhari, 2004. "Adaptative Monte Carlo Method, A Variance Reduction Technique," Monte Carlo Methods and Applications, De Gruyter, vol. 10(1), pages 1-24, March.
    18. Hernan P. Awad & Peter W. Glynn & Reuven Y. Rubinstein, 2013. "Zero-Variance Importance Sampling Estimators for Markov Process Expectations," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 358-388, May.
    19. Ye Xiao & Xiaoqun Wang, 2019. "Enhancing Quasi-Monte Carlo Simulation by Minimizing Effective Dimension for Derivative Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 343-366, June.
    20. Fredrik Åkesson & John P. Lehoczky, 2000. "Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities," Management Science, INFORMS, vol. 46(9), pages 1171-1187, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9108-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.