In derivative pricing and hedging, the consistency between the price and Greek surfaces (i.e., the Greek surfaces can be obtained by differentiating the price surface) is important in stabilizing the balance sheet and reducing the hedging cost. To build consistent surfaces of the price and Greeks for real-time decisions, we propose to use the gradient-enhanced stochastic kriging method, based on the data collected through extensive simulation experiments conducted when the market is closed. In addition to the naturally guaranteed consistency, we prove that the constructed price and Greek surfaces are more accurate than those constructed separately using stochastic kriging. Besides the consistency between the price and Greeks, we show that the partial differential equation relation between the price and Greeks, implied by the famous Feynman-Kac formula, can also be used to further improve the accuracy of the constructed surfaces. The numerical studies show that our proposed metamodeling methods work well for derivative pricing and hedging. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72161160340, 72293562, 72121001, 72031006, and 72171060]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0292 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0292 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We consider a problem of ranking and selection via simulation in the context of personalized decision making, in which the best alternative is not universal, but varies as a function of some observable covariates. The goal of ranking and selection with covariates (R&S-C) is to use simulation samples to obtain a selection policy that specifies the best alternative with a certain statistical guarantee for subsequent individuals upon observing their covariates. A linear model is proposed to capture the relationship between the mean performance of an alternative and the covariates. Under the indifference-zone formulation, we develop two-stage procedures for both homoscedastic and heteroscedastic simulation errors, respectively, and prove their statistical validity in terms of average probability of correct selection. We also generalize the well-known slippage configuration and prove that the generalized slippage configuration is the least favorable configuration for our procedures. Extensive numerical experiments are conducted to investigate the performance of the proposed procedures, the experimental design issue, and the robustness to the linearity assumption. Finally, we demonstrate the usefulness of R&S-C via a case study of selecting the best treatment regimen in the prevention of esophageal cancer. We find that by leveraging disease-related personal information, R&S-C can substantially improve patients’ expected quality-adjusted life years by providing a patient-specific treatment regimen.