Unbiased Estimation with Square Root Convergence for SDE Models

Chang-Han Rhee () and Peter W. Glynn ()
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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

Operations Research, 2015, vol. 63, issue 5, 1026-1043

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.

Keywords: unbiased estimation; exact estimation; square root convergence rate; stochastic differential equations (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (30)

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