台指選擇權近年來已逐漸發展成一成熟市場。本文採用快速傅利葉轉換的方法，比較 Heston (1993)年的連續型隨機波動率模型、VG模型、Ad Hoc BS 模型及BS 等四個模型。
    實証結果顯示，MAE與MAPE在樣本外一日近月買權的訂價效率以AHBS 模型最好，遠月及整體部份大致以SV模型表現較好。而樣本外七日除了近、遠月及整體的深價內買權以VG模型表現較優外，其餘大部分仍以SV模型表現最好。RMSE則顯示除了樣本外七日遠月無一致性結論外，其他幾乎以SV模型最小，顯示SV模型的誤差穩性性。此外，MPE顯示SV模型有高估價外買權及價內賣權並低估價內買權及價外賣權的傾向，此種風險中立機率集中於左尾的表現，推估原因與波動率和標的資產報酬率之相關係數為負值有關。
    誤差來源分析部份，採用的誤差因子包括價性、價性平方項、到期期間與利率。實證結果顯示，除了樣本外七日賣權在價性及利率等兩項因子之迴歸斜率係數不顯著外，其餘係數皆顯著。同時也發現SV模型可以改善波動率微笑。

In the last decade, TXO has become one of the most famous trading derivatives. This article compares empirical performances of four option pricing models: (1). Heston’s continuous-time stochastic volatility model, (2). Madan et al.’s variance gamma model, (3).Dumas et al.’s ad hoc BS model, and (4). BS model. 
  Our empirical results for one day ahead out–of-sample show that near-month call options perform best, while SV model outperforms the others in the all sample case and forward month case. For one week ahead out–of-sample performances, I find that except deep out- and out-of-the money near-month put options and call options, VG model shows the best performances in deep-in-the-money contracts and SV the others. We also find that SV model generally has min RMSE values that mean large pricing error occurs least. However, we can see SV model also overprices out-of-the-money calls and in-the-money puts and underprices out-of-the-money puts and in-the-money calls from MPE. This type of mispricing indicates an unusual concentration of probability mass in the left tail of the risk neutral distribution of the index returns, part of which can result from negative correlation between index returns and volatility.
  In terms of error regression analysis, after taking into account the four error factors (maturity, interest, moneyness and its square term), all slope parameters are significant except moneyness and interest rate in one week ahead put options. Otherwise, we also find SV model improves the volatility smile.

目錄
第一章緒論1
第一節研究背景1
第二節研究目的3
第三節研究流程4
第二章文獻回顧5
第一節各種波動率模型相關文獻5
第二節隨機波動率模型之實證18
第三章研究方法23
第一節三種具封閉解的隨機與定態波動率模型23
第二節快速傅利葉轉換30
第三節估計方法36
第四節預測能力指標37
第五節誤差來源分析39
第四章實證結果41
第一節資料來源及處裡方法41
第二節各模型之誤差分析47
第三節誤差來源分析64
第五章結論與建議68
第一節研究結論68
第二節後續建議71
參考文獻72
附錄75

表目錄
表 4-1-1	台灣加權股價指數買權與賣權樣本特性表43
表 4-2-1	BS隱含波動率表45
表 4-2-2	BS、VG、AHBS、SV模型買權參數表46
表 4-2-3	BS、VG、AHBS、SV模型賣權參數表46
表 4-2-4	近月份台指買權與賣權模型樣本內誤差表	49
表 4-2-5	遠月份台指買權與賣權模型樣本內誤差表	50
表 4-2-6	台指買權與賣權模型樣本內誤差表(all)51
表 4-2-7	近月份台指買權與賣權模型樣本外一日誤差表54
表 4-2-8	遠月份台指買權與賣權模型樣本外一日誤差表55
表 4-2-9	台指買權與賣權模型樣本外一日誤差表(all)56
表 4-2-10	樣本外一日模型定價效率整理57
表 4-2-11	近月份台指買權與賣權模型樣本外七日誤差表60
表 4-2-12	遠月份台指買權與賣權模型樣本外七日誤差表61
表 4-2-13	台指買權與賣權模型樣本外七日誤差表(all)62
表 4-2-14	樣本外七日模型定價效率整理63
表 4-3-1	台指買權與賣權模型樣本外一日誤差迴歸分析表66
表 4-3-2	台指買權與賣權模型樣本外七日誤差迴歸分析表67
附錄     臺灣證券交易所股價指數選擇權契約規格75

圖目錄
圖 1-3-1	研究流程圖4
圖 4-1-1	台灣加權股價指數走勢圖44

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