Large-sample theory for standardized time series: an overview
WSC '85 Proceedings of the 17th conference on Winter simulation
Estimating security price derivatives using simulation
Management Science
Large-sample results for batch means
Management Science
An overview of derivative estimation
WSC '91 Proceedings of the 23rd conference on Winter simulation
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Estimating Quantile Sensitivities
Operations Research
Kernel Estimation of the Greeks for Options with Discontinuous Payoffs
Operations Research
A brief introduction to optimization via simulation
Winter Simulation Conference
Monte Carlo estimation of value-at-risk, conditional value-at-risk and their sensitivities
Proceedings of the Winter Simulation Conference
Asymptotic properties of kernel density estimators when applying importance sampling
Proceedings of the Winter Simulation Conference
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A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous. In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res.57(1) 118--130]. We show that the estimator is consistent and follows a central limit theorem for simulation outputs from both terminating and steady-state simulations, and the optimal rate of convergence of the estimator is n-2/5 where n is the sample size. We further demonstrate how to use importance sampling to accelerate the rate of convergence of the estimator to n-1/2, which is the typical rate of convergence for statistical estimation. We illustrate the performances of our estimators and compare them to other well-known estimators through several examples.