Variance comparison between infinitesimal perturbation analysis and likelihood ratio estimators to stochastic gradient

Zhenyu Cui, Yanchu Liu, Ruodu Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We theoretically compare variances between the Infinitesimal Perturbation Analysis (IPA) estimator and the Likelihood Ratio (LR) estimator to Monte Carlo gradient for stochastic systems. The results presented in Cui et al. (2020) [2] on variance comparison between these two estimators are substantially improved. We also prove a practically interesting result that the IPA estimators to European vanilla and arithmetic Asian options' Delta, respectively, have smaller variance when the underlying asset's return process is independent with the initial price and square integrable.

Original languageEnglish
Pages (from-to)199-204
Number of pages6
JournalOperations Research Letters
Volume50
Issue number2
DOIs
StatePublished - Mar 2022

Keywords

  • Infinitesimal perturbation analysis
  • Likelihood ratio
  • Option delta
  • Stochastic gradient
  • Variance comparison

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