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Implementing de-biased estimators using mixed sequences

Author

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  • Polala Arun Kumar

    (Department of Mathematics, Florida State University, TallahasseeFL 32306-4510, USA)

  • Ökten Giray

    (Department of Mathematics, Florida State University, TallahasseeFL 32306-4510, USA)

Abstract

We describe an implementation of the de-biased estimator using mixed sequences; these are sequences obtained from pseudorandom and low-discrepancy sequences. We use this implementation to numerically solve some stochastic differential equations from computational finance. The mixed sequences, when combined with Brownian bridge or principal component analysis constructions, offer convergence rates significantly better than the Monte Carlo implementation.

Suggested Citation

  • Polala Arun Kumar & Ökten Giray, 2020. "Implementing de-biased estimators using mixed sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 26(4), pages 293-301, December.
    • Handle: RePEc:bpj:mcmeap:v:26:y:2020:i:4:p:293-301:n:5
    DOI: 10.1515/mcma-2020-2075
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    References listed on IDEAS

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    1. Okten, Giray & Eastman, Warren, 2004. "Randomized quasi-Monte Carlo methods in pricing securities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2399-2426, December.
    2. 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.
    3. 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.
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