臺灣博碩士論文加值系統

鑑於波動度無論在金融衍生性商品訂價、風險值的估算、投資組合的選擇以及動態避險策略的推估上皆有密切的關係，因此本文在常態分配與一般化誤差分配（GED）兩種分配下，驗證GARCH、GJR-GARCH、E-GARCH、I-GARCH與Q-GARCH等五種傳統計量模型與其結合類神經模型之五種複合式模型在波動度預測上之能力，且為解決真實波動度（true volatility)之代理問題（volatility proxy），本文導入以日內60分鐘報酬最高與最低計算之Realized Range-Based Volatility，並分別以MAE、MSE、MME與VaRE做為預測能力衡量指標，另外並以預測之波動度代入Black-Sholes公式反推出選擇權理論價格與真實價格計算其MAE，最後加入SPA (Superior Predictive Ability)檢定，以改善大量模型比較所可能存在最佳模型選取錯誤之疑問，期望找出一個可以精準預測波動度之模型。實證結果為：台灣日資料的股票波動，以類神經結合Q-GARCH模型預測能力最佳，I-GARCH最差；而在選擇權驗證方面，其結果完全相反，以類神經結合I-GARCH模型預測能力最佳。顯示由統計之觀點與財務之觀點來看波動度預測能力會得到不同的結論，而唯一可以確定的就是無論在損失函數方面與選擇權驗證方面，類神經模型之導入皆可增進模型之預測能力。

We compare the predictive performance of various GARCH family models and Neural Networks. The models are compared out-of-sample using Taiwan Stock Exchange Capitalization Weighted Stock Index（TAIEX）data. We substitute the Realized Range-Based Volatility for the latent true volatility and choose six statistical loss functions to compare the predictive performance. We also use the forecasting volatilities into Black-Scholes formula to evaluate the theoretical option prices and compare with real option prices. To control for the fact that as the number of models increase, so does the probability of finding superior predictive ability among the collection of models, we implement the Superior Predictive Ability Test of Hansen（2005）.
　　We find that, for four loss function, Neural Networks nested Q-GARCH model seems dominate. For two VaR based loss function, GJR-GARCH and GARCH models are preferred. For option pricing, Neural Networks nested I-GARCH model, which performs the worst in the six loss function, seems to be the best performer.

表目錄 iv
圖目錄 v
第一章　緒 論 1
第一節　研究背景與動機 1
第二節 研究目的 3
第三節 研究架構 4
第二章　文獻回顧 6
第一節　使用GARCH類模型預測波動之文獻 6
第二節 使用類神經模型預測波動之文獻 13
第三章　研究方法 17
第一節　單根檢定 17
第二節　ARCH效果檢定 21
第三節　條件變異數不對稱檢定 24
第四節　誤差分配之理論基礎 26
第五節　Realized Range-Based Volatility 28
第六節　條件變異數模型 29
第七節　類神經網路（Artificial Neural Networks） 34
第八節　預測績效的評估標準 37
第九節　Black-Scholes 選擇權評價模型 40
第十節　Superior Predictive Ability Test 42
第四章　實證結果分析 44
第一節　研究對象 44
第二節　基本統計量分析 46
第三節　單根檢定 47
第四節　ARCH效果檢定 49
第五節　條件變異數不對稱檢定 50
第六節 各種模型之參數估計結果 51
第七節　預測績效之比較 53
第五章　結論 73
參 考 文 獻 75
一、國外文獻 75
二、國內文獻 79


表目錄
【表4 - 1 - 1】依價內外程度分類之樣本個數表—買權 45
【表4 - 1 - 2】依價內外程度分類之樣本個數表—賣權 45
【表4 - 2 - 1】股價指數日報酬率之基本統計量 46
【表4 - 3 - 1】股價指數原始序列之單根檢定 48
【表4 - 3 - 2】股價指數日報酬率之單根檢定(差分項) 48
【表4 - 4 - 1】ARCH效果檢定分析 49
【表4 - 5 - 1】條件變異數不對稱檢定 50
【表4 - 6 - 1】NORMAL分配下各模型之估計結果 52
【表4 - 6 - 2】GED分配下各模型之估計結果 52
【表4 - 7 - 1】常態分配下預測結果MAE之SPA TEST 53
【表4 - 7 - 2】GED分配下之預測結果MAE之SPA TEST 54
【表4 - 7 - 3】常態分配下之預測結果之MSE之SPA TEST 55
【表4 - 7 - 4】GED分配下之預測結果之MSE之SPA TEST 55
【表4 - 7 - 5】常態分配下之預測結果MME(O)之SPA TEST 56
【表4 - 7 - 6】GED分配下之預測結果MME(O)之SPA TEST 57
【表4 - 7 - 7】常態分配下預測結果MME(U)之SPA TEST 58
【表4 - 7 - 8】GED分配下預測結果MME(U)之SPA TEST 58
【表4 - 7 - 9】常態分配下預測結果VaRED之SPA TEST 60
【表4 - 7 - 10】GED分配下預測結果VaRED之SPA TEST 60
【表4 - 7 - 11】常態分配下預測結果VaREC之SPA TEST 61
【表4 - 7 - 12】GED分配下預測結果VaREC之SPA TEST 62
【表4 - 8 - 1】常態分配下買權價平之SPA TEST 63
【表4 - 8 - 2】GED分配下買權價平之SPA TEST 64
【表4 - 8 - 3】常態分配下買權價內之SPA TEST 65
【表4 - 8 - 4】GED分配下買權價內之SPA TEST 65
【表4 - 8 - 5】常態分配下買權價外之SPA TEST 66
【表4 - 8 - 6】GED分配下買權價外之SPA TEST 67
【表4 - 8 - 7】常態分配下賣權價平之SPA TEST 68
【表4 - 8 - 8】GED分配下賣權價平之SPA TEST 68
【表4 - 8 - 9】常態分配下賣權價內之SPA TEST 69
【表4 - 8 - 10】GED分配下賣權價內之SPA TEST 70
【表4 - 8 - 11】常態分配下賣權價外之SPA TEST 71
【表4 - 8 - 12】GED分配下賣權價外之SPA TEST 71


圖目錄
【圖 1】研究流程圖 5
【圖 2】無隱藏層之類神經模型示意圖 35
【圖 3】含隱藏層之類神經模型示意圖 36

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