Managing Simulation Uncertainty in Percentiles and Value-at-Risk

Accurate estimates of simulation uncertainty around percentiles and Value-at-Risk (VaR) measures are important for various practical applications in insurance, pensions and banking. Managing simulation uncertainty requires using an adequate number of scenarios to produce reliable risk estimates. The simplest approach for determining simulation uncertainty would be to reperform the calculations many times (with a different seed or via bootstrapping) and measure the variation in the outcomes of the re-simulated estimates. However, given that in practice often 100,000 scenarios or more are used, this approach is quite impractical. In this article we describe an alternative method based on an ‘in-sample’ estimate of the simulation error. This ‘in-sample’ estimate relies solely on the original simulations to determine the uncertainty around the percentile, making it practical to compute.