The expected-based value-at-risk and expected shortfall using quantile and expectile with application to electricity market data

Abstract

Forecasting risk measures in order to minimize and prevent a worse risk is an important and challenging task in quantitative risk management. Methodology and assessment of forecast accuracy are still developed to give a better risk measure forecast. In this paper, we provide a simple procedure to forecast expected-based risk measures of Value-at-Risk (VaR) and Expected Shortfall (ES). These risk measures may be determined by not only quantile but also expectile. By extending the Historical Simulation (HS) method and adopting the Monte Carlo (MC) principle, we build alternative algorithms without disregarding the (estimated) probability and/or distribution function(s) of the loss distribution. Based on the illustration for return data from New South Wales (NSW) Australian and Iranian electricity markets, it is found that our proposed method gives the expected-based risk measure forecast with better accuracy, instead of using the conventional HS method. The accuracy is getting higher when we consider the model able to capture the features of heavy-tailedness and conditional heteroscedasticity in the data.