Variance Comparison between Infinitesimal Perturbation Analysis and Likelihood Ratio Estimators to Stochastic Gradient
Operations Research Letters forthcoming
16 Pages Posted: 2 Jul 2021 Last revised: 6 Feb 2022
Date Written: June 29, 2021
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 [1] 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.
Keywords: Stochastic Gradient, Infinitesimal Perturbation Analysis, Likelihood Ratio, Variance Comparison, Option Delta
JEL Classification: C15, C18, G13
Suggested Citation: Suggested Citation