臺灣博碩士論文加值系統

為了精準預測未來波動性，目前已有多種波動性預測的模型，然而由於各波動性預測模型對波動性預測的能力差異性頗大，所以本文重新以四種常用的「歷史波動性模型」、「隱含波動性模型」、「GARCH波動性模型」、「GARCH+JUMP波動性模型」所求出的波動性估計值，代入B-S定價模型求出B-S模型價格後與市價進行價格誤差分析，重新驗證各波動性的預測能力。
研究發現不論以MAE、MAPE、RMSE的價格誤差衡量指標來衡量市價與模型價格的誤差，結果都顯示BS_IV的預測能力最好。雖然BS_GARCH是目前較受大家廣泛使用的波動性模型；而BS_GARCHJUMP則是迎合日益多變的金融環境下所衍生出來的新波動性模型。但此兩種模型在本文用MAE與MAPE衡量誤差指標的實證研究中，顯示加入Jump觀念的GARCHJUMP波動性模型，其預測能力比GARCH模型大為提昇。表示GARCHJUMP波動性模型比GARCH波動性模型更能反應不同權證JUMP的程度。因此建議後續波動性的研究一定要導入JUMP的觀念，才能更完整掌握權證的波動，提高對未來波動性預測的準確性。

To predict the volatility of stock market more precisely，various volatility-predicted models have been built-up. However, the results of those models are quite different. In this thesis, we apply four widely held predict models for testify the model capability of predicted accuracy; those are 「historical volatility model」、「implied volatility model」、「GARCH volatility model」、「GARCH-jump volatility model」 . We following three steps, first, calculate the estimate volubility values in those models, and then use the B-S pricing model to develop the prices of B-S model; finally, to exam and analysis the difference between estimated value and market price.
In this study, after test the difference between estimated value and actual price by MAE、MAPE、RMSE pricing margin standard, we find out the BS-IV model has the best predict ability. In general, BS-GARCH is the most popular predict model, while BS-GARCH-jump is new predict model to adapt the changeful financial environment and instrument. After exemplify BS-GARCH and BS-GARCH-jump model by MAE and MAPE formulas, GARCH-jump model get better results by involve jump idea. Therefore, we can conclude that GARCH-jump model can reflect the jump volatility of options. For further study, we assert that violability model research must contain the jump idea to notify the volatility of option and arise the ability to predict the volatility.

第一章 緒論
第一節 研究動機 ………………………………………………………………1
第二節 研究目的 ………………………………………………………………2
第三節 研究架構 ………………………………………………………………4
第二章 認購權證簡介
第一節 權證的種類……………………….……………………………………7
第二節 認購權證的特色與風險………..…………………...………………10
第三節 認購權證的價值.…………….………………….…………….………12
第四節 認購權證價值的影響因素 .……………….……………………….14
第三章 文獻回顧
第一節 GARCH 模型………………………………………………………..20
第二節 隱含波動性模型……………………………………………………..24
第三節 jump-diffusion 模型………………………………………………...28
第四節 GARCH - jump-diffusion 模型……………………………………30
第四章 研究方法
第一節 波動性估計模型……………..…………………….………………….31
第二節 模型績效指標……………………………………………………...….42
第五章 實證結果與分析
第一節 資料來源與處理 ……………….…………………………………….44
第二節 實證步驟 ……………………………………………………………..45
第三節 實證結果 ……………………………………………………………..46
第六章 結論與建議 ……..………………………………………………………..54
參考文獻 ……………………………………………………………………………57

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