In this paper, stochastic kriging (SK) is considered as a metamodeling tool to capture risk-related properties of complex stochastic system outputs. To better assess the tail behavior of the underlying distribution of a system output, we specifically focus on global prediction of value-at-risk and conditional value-at-risk. Going beyond the standard SK framework intended for metamodeling of mean response surfaces, we rethink the original formulation to allow for the flexibility of utilizing different estimation methods for metamodel construction. The resulting impact on the predictive performance of SK is examined in detail. In parallel with the study by Chen et al. [Chen X, Ankenman BE, Nelson BL (2013) Enhancing stochastic kriging metamodels with gradient estimators. Oper. Res. 61(2): 512-528], we further consider the situation in which noisy gradient information can be incorporated into SK metamodel construction and prediction. The theoretical results are illustrated by two numerical examples.