IDEAS home Printed from
   My bibliography  Save this article

Efficient Risk Estimation via Nested Sequential Simulation


  • Mark Broadie

    () (Graduate School of Business, Columbia University, New York, New York 10027)

  • Yiping Du

    () (Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ciamac C. Moallemi

    () (Graduate School of Business, Columbia University, New York, New York 10027)


We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the probability of a large loss, and we propose a new algorithm to estimate this risk. Our algorithm sequentially allocates computational effort in the inner simulation based on marginal changes in the risk estimator in each scenario. Theoretical results are given to show that the risk estimator has a faster convergence order compared to the conventional uniform inner sampling approach. Numerical results consistent with the theory are presented. This paper was accepted by Gérard Cachon, stochastic models and simulation.

Suggested Citation

  • Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
  • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:6:p:1172-1194

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
    2. Vadim Lesnevski & Barry L. Nelson & Jeremy Staum, 2007. "Simulation of Coherent Risk Measures Based on Generalized Scenarios," Management Science, INFORMS, vol. 53(11), pages 1756-1769, November.
    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. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Julien Vedani & Fabien Ramaharobandro, 2013. "Continuous compliance: a proxy-based monitoring framework," Papers 1309.7222,, revised Dec 2013.
    2. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243,
    3. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
    4. repec:eee:insuma:v:76:y:2017:i:c:p:87-94 is not listed on IDEAS
    5. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    6. Julien Vedani & Fabien Ramaharobandro, 2013. "Continuous compliance: a proxy-based monitoring framework," Working Papers hal-00866531, HAL.
    7. Helin Zhu & Tianyi Liu & Enlu Zhou, 2015. "Risk Quantification in Stochastic Simulation under Input Uncertainty," Papers 1507.06015,, revised Dec 2017.
    8. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204,
    9. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197,, revised Feb 2018.
    10. Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013. "The Risk Map: A new tool for validating risk models," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3843-3854.
    11. Halis Sak & .Ismail Bac{s}ou{g}lu, 2015. "Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk," Papers 1510.01593,
    12. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310,, revised Sep 2015.
    13. Ankirchner, Stefan & Schneider, Judith C. & Schweizer, Nikolaus, 2014. "Cross-hedging minimum return guarantees: Basis and liquidity risks," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 93-109.


    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:inm:ormnsc:v:57:y:2011:i:6:p:1172-1194. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.