Two-level simulation of expected shortfall: Confidence intervals, efficient simulation procedures, and high-performance computing

We develop and evaluate a two-level simulation procedure that produces a confidence interval for expected shortfall. The outer level of simulation generates financial scenarios while the inner level estimates expected loss conditional on each scenario. Our procedure uses the statistical theory of empirical likelihood to construct a confidence interval, and tools from the ranking-and-selection literature to make the simulation efficient.;Parameters that govern the behavior of the simulation procedures are important to the effectiveness of sophisticated simulation. A parameter tuning method for a two-level simulation with screening is discussed. A special procedure is introduced to predict the behavior of the two-level simulation based on historical data or a pilot simulation. A hybrid method of grid search and nonlinear convex local optimization techniques is adopted to find suitable input parameters to optimize the forecast performance of the two-level simulation.;On the other hand, we accelerate the simulation by applying the new development of parallel computing into the two-level simulation with screening. A hybrid of multi-core CPU and multiple GPUs is adopted to hasten the computational efficiency of two-level simulation with screening. Currently, we can shorten the simulation time by a factor of 70 compared with serial implementation.