TY - JOUR
T1 - Variance comparison between infinitesimal perturbation analysis and likelihood ratio estimators to stochastic gradient
AU - Cui, Zhenyu
AU - Liu, Yanchu
AU - Wang, Ruodu
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - Infinitesimal perturbation analysis
KW - Likelihood ratio
KW - Option delta
KW - Stochastic gradient
KW - Variance comparison
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U2 - 10.1016/j.orl.2022.01.012
DO - 10.1016/j.orl.2022.01.012
M3 - Article
AN - SCOPUS:85124283389
SN - 0167-6377
VL - 50
SP - 199
EP - 204
JO - Operations Research Letters
JF - Operations Research Letters
IS - 2
ER -