Nonparametric Prediction Interval for Conditional Expected Shortfall Admitting a Location-Scale Model using Bootstrap Method

Abstract

In financial risk management, the expected shortfall is a popular risk measure which is often considered as an alternative to Value-at-Risk. It is defined as the conditional expected loss given that the loss is greater than a given Value-at-Risk (quantile). In this paper at hand, we have proposed a new method to compute nonparametric prediction bands for Conditional Expected Shortfall for returns that admits a location-scale model. Where the location (mean) function and scale (variance) function are smooth, the error term is unknown and assumed to be uncorrelated to the independent variable (lagged returns). The prediction bands yield a relatively small width, indicating good performance as depicted in the literature. Hence, the prediction bands are good especially when the returns are assumed to have a location-scale model.