樣本外預測評估金融風險模型

Abstract

本報告採用兩個股票市場指數Russell 2000和Swiss Market Index來評估兩市場的風險及表現。首先，我們使用R套件``quantmod''從Yahoo Finance中截取日報酬率，我們應用六個風險模型來對模型參數推論，並預測波動率和風險值。 以下用英文縮寫:RiskMetrics、GARCH、GARCH in Mean、IGARCH、GJR-GARCH、EGARCH。最後兩個模型為不對稱異質模型。 我們也考慮了四個誤差機率分佈，其中包括:常態分佈，Student’s t分佈，skew Student’s t分佈，廣義誤差(GED)分佈，樣本內資料期間是從2000年1月4日到2018年8月30月，並且使用滾動窗口的方法來進行一步的預測，要預測的樣本外期間為2018年9月1日至2019年12月25日，我們評估所有的風險模型是否其違反率接近顯著水準。檢定方法我們使用兩種回溯測試方法(無條件涵蓋檢定法和有條件涵蓋檢定法)個別用於1%和5%的水準做決策；最後的分析結果顯示，帶有偏態的Student’s error的EGARCH模型在1%水準下是兩個股票市場中的最佳模型，依據分析結果可以得知，帶有偏態的Student’s error可以很好的解釋資料中有偏態和厚尾的特徵。

This report evaluates risk performance based on two stock market indexes, Russell 2000 and Swiss Market Index. We use the R package ``quantmod'' to extract daily returns from Yahoo Finance. We employ six risk models to make inference model parameters and forecast volatility and Value-at-Risk. There are RiskMetrics, GARCH model, GARCH in Mean, integrated GARCH, GJR-GARCH, and exponential GARCH models. The last two models are known as the asymmetric heteroscedastic models. Four error probability distributions are considered, included Normal, Student’s t, skew Student’s t and generalized error distributions. We consider an in-sample period from January 4, 2000 to August 30, 2018. We focus on one-step-ahead forecasts based on a rolling window approach. The out-of-sample period covers from September 1, 2018 to December 25, 2019. We provide violation rates for all risk models, which should be close to the nominal level . Two backtests, the unconditional coverage test and the conditional coverage test, are used for both 1% and 5% levels. The analysis results show that EGARCH with skew Student’s error is the best model in both stock markets at the 1% level. This EGARCH with skew Student’s error can well explain the characteristics of skewness and thick tail.