We develop and evaluate a two-level simulation procedure that produces a confidence interval for expectedshortfall. The outer level of simulation generates financial scenarios while the inner level estimates expectedloss 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 effectivenessof sophisticated simulation. A parameter tuning method for a two-level simulation withscreening 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 inputparameters to optimize the forecast performance of the two-level simulation.
On the other hand, we boost the simulation efficiency by applying the new development of parallel computing into the Two-level Simulation with Screening. The implementation with OpenMP on multi-cores CPU and that with CUDA on many cores GPU are realized. A hybrid of multi-cores CPU and multiple GPUs is adopted to hasten thecomputational efficiency of Two-level Simulation with Screening. Currently, we can shorten the simulation time by a factor of five compared with serial implementation. More optimization is going to be done in the short future. The computational efficency is expected to be improved 50-fold or so.