Stochastic kriging for efficient nested simulation of expected shortfall

We use stochastic kriging, a metamodeling technique, to speed up nested simulation of expected shortfall, a portfolio risk measure. Evaluating a risk measure of a portfolio that includes derivative securities may require nested Monte Carlo simulation. 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: it is not necessary to perform innerlevel simulation in every scenario. 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.