使用實際波動率及FZ損失函數來預測預期損失及風險值

Forecasting Expected Shortfall and Value-at-Risk with Realized Variance Measures and the FZ Loss

預期損失（expected shortfall，ES）和風險值（value at risk，VaR）是經濟學及財務金融中使用最廣泛的兩種衡量風險的指標。在本文中，我們將實際波動率加入到這兩種風險衡量指標的結構模型中。我們使用Fissler and Ziegel（2016）所提出的一種一致性損失函數來進行半參數模型估計，並提出了一種有效且穩定的兩階段方法來進行估計程序。我們將估計的結構模型與一些現有的方法（包括一些最近所提出的新模型），進行的樣本外預測表現之比較。與這些現有方法相比，我們發現擁有實際波動率的結構模型可提供更好的預期損失和風險值預測。使用模型平均的分析進一步顯示了，將來自不同方法的資訊進行匯總可以提高預測的績效，並且在不同的績效指標之間提供更一致的比較結果。而對於產生較為優越的模型平均預測，擁有實際波動率之模型所產生的資訊則是不可或缺的。

Expected shortfall (ES) and value at risk (VaR) are two of the most widely used risk measures in economics and finance. In this paper, we incorporate realized variance measures into structural models for the two risk measures. Our estimation procedure is semiparametric and relies on using a class of consistent loss functions proposed by Fissler and Ziegel (2016). We develop an efficient and stable two-stage method to implement the estimations. We then compare performances of out-of-sample forecasts from the estimated structural models with some existing methods, including several recently proposed novel models. We demonstrate that the proposed structure models with realized variance measures overall deliver superior forecasts of ES and VaR for major stock indices than the considered existing methods. An analysis of model averaging further shows that aggregating information from different methods can improve performances of the forecasts, and information from models with realized variance measures is indispensable for generating a superior model averaging forecast.