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

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China.

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

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

Cui, Zhenyu and Liu, Yanchu and Wang, Ruodu, Variance Comparison between Infinitesimal Perturbation Analysis and Likelihood Ratio Estimators to Stochastic Gradient (June 29, 2021). Operations Research Letters forthcoming, Available at SSRN: https://ssrn.com/abstract=3876623 or http://dx.doi.org/10.2139/ssrn.3876623

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Yanchu Liu

Lingnan (University) College, Sun Yat-sen University, Guangzhou, China. ( email )

Haizhu District,
Guangzhou, China.
Guangzhou, Guangdong 510275
China

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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