Estimating expected shortfall with stochastic kriging

We present an efficient two-level simulation procedure which uses stochastic kriging, a metamodeling technique, to estimate expected shortfall, a portfolio risk measure. The outer level simulates financial scenarios and the inner level of simulation estimates the portfolio value given a scenario. Spatial metamodeling enables inference about portfolio values in a scenario based on inner-level simulation of nearby scenarios, reducing the required computational effort. Because expected shortfall involves the scenarios that entail the largest losses, our procedure adaptively allocates more computational effort to inner-level simulation of those scenarios, which also improves computational efficiency.