Unbiased estimation with square root convergence for SDE models

Chang-Han Rhee, Peter W. Glynn

Research output: Contribution to journalArticlepeer-review

103 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1026-1043
Number of pages18
JournalOperations Research
Issue number5
StatePublished - Sep 1 2015


  • Exact estimation
  • Square root convergence rate
  • Stochastic differential equations
  • Unbiased estimation

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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