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Unbiased Estimation with Square Root Convergence for SDE Models

Author

Listed:
  • Chang-Han Rhee

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Peter W. Glynn

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

In many settings in which Monte Carlo methods are applied, there may be no known algorithm for exactly generating the random object for which an expectation is to be computed. Frequently, however, one can generate arbitrarily close approximations to the random object. We introduce a simple randomization idea for creating unbiased estimators in such a setting based on a sequence of approximations. Applying this idea to computing expectations of path functionals associated with stochastic differential equations (SDEs), we construct finite variance unbiased estimators with a “square root convergence rate” for a general class of multidimensional SDEs. We then identify the optimal randomization distribution. Numerical experiments with various path functionals of continuous-time processes that often arise in finance illustrate the effectiveness of our new approach.

Suggested Citation

  • Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:5:p:1026-1043
    DOI: 10.1287/opre.2015.1404
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    References listed on IDEAS

    as
    1. Nan Chen & Zhengyu Huang, 2013. "Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 591-616, August.
    2. McLeish, Don, 2011. "A general method for debiasing a Monte Carlo estimator," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 301-315, December.
    3. Michael B. Giles & Lukasz Szpruch, 2012. "Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L\'{e}vy area simulation," Papers 1202.6283, arXiv.org, revised May 2014.
    4. Chang-han Rhee & Peter W. Glynn, 2012. "A new approach to unbiased estimation for SDE's," Papers 1207.2452, arXiv.org.
    5. Kay Giesecke & Dmitry Smelov, 2013. "Exact Sampling of Jump Diffusions," Operations Research, INFORMS, vol. 61(4), pages 894-907, August.
    6. P. E. Kloeden & Eckhard Platen & I. W. Wright, 1992. "The approximation of multiple stochastic integrals," Published Paper Series 1992-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Peter W. Glynn & Ward Whitt, 1992. "The Asymptotic Efficiency of Simulation Estimators," Operations Research, INFORMS, vol. 40(3), pages 505-520, June.
    8. Bernard Lapeyre & Emmanuel Temam, 2001. "Competitive Monte Carlo methods for the pricing of Asian options," Post-Print hal-01667057, HAL.
    9. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
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