臺灣博碩士論文加值系統

本研究比較隨機波動與隨機利率 (Stochastic Volatility and Stochastic Interest, SVSI)與固定波動度與固定利率 (Deterministic Volatility and Deterministic Interest, DVDI) 模型的評價差異。數值分析結果顯示，SVSI評價模型的誤差表現較DVDI評價模型來的小。接著，我們以「美式認售權證」價格之市場資料進行參數估計與評價分析。實證結果亦顯示，SVSI評價模型實證的績效表現都較DVDI評價模型佳，因此SVSI模型在美式認售權證的評價上較DVDI模型具有優勢，對於投資人的投資與避險、公司的風險管理上能提供較好的決策。

This study compares pricing models of the SVSI (Stochastic Volatility and Stochastic Interest) and DVDI (Deterministic Volatility and Deterministic Interest). For numerical analysis, the result shows that the pricing error of SVSI is smaller than the error of DVDI. Next, we take the market data of American put warrant to estimate the parameters of models and analyze the pricing performance. Empirical results reveal that the performance of SVSI is better than DVDI. Hence the SVSI model takes an advantage of American put warrant to the DVDI. Furthermore, the SVSI model provides a better decision for the investment and hedging of the investors and the risk management of the companies.

中文摘要 ........................................................................................................................... i
英文摘要 .......................................................................................................................... ii
表目錄 .............................................................................................................................. v
圖目錄 ............................................................................................................................. vi
壹、緒論 .......................................................................................................................... 1
一、研究背景與動機 .................................................................................................. 1
二、研究架構 .............................................................................................................. 5
貳、文獻回顧 .................................................................................................................. 7
一、美式選擇權評價方法之發展 .............................................................................. 7
二、波動度估計相關文獻 .......................................................................................... 9
參、研究方法 ................................................................................................................ 11
一、 DVDI評價模型介紹 ..................................................................................... 11
(一) Black & Scholes 評價模型 ............................................................................ 11
(二) 二元樹評價模型 ............................................................................................ 14
(三) 有限差分法 .................................................................................................... 17
二、SVSI模型評價模型介紹 ................................................................................... 19
三、選擇權模型之參數估計方法 ............................................................................ 20
四、「美式認售權證」績效衡量方法 .................................................................... 22
(一) 均方誤差 (Mean Square Error) ..................................................................... 22
(二) 平均絕對誤差 (Mean Absolute Error).......................................................... 22
(三) 平均絕對百分比誤差 (Mean Absolute Percentage Error) ........................... 23
肆、數值分析 ................................................................................................................ 24
iv
一、LSM模型介紹 ................................................................................................... 24
二、DVDI、SVSI模型與LSM模型之比較 ........................................................... 24
二、DVDI、SVSI模型誤差分析 ............................................................................. 29
伍、實證分析 ................................................................................................................ 31
一、資料來源 ............................................................................................................ 31
二、DVDI、SVSI模型參數估計 ............................................................................. 31
三、績效評估日的選取 ............................................................................................ 32
四、實證結果 ............................................................................................................ 32
陸、結論與建議 ............................................................................................................ 36
一、結論 .................................................................................................................... 36
二、後續研究及建議 ................................................................................................ 37
參考文獻 ........................................................................................................................ 38
附錄 ................................................................................................................................ 42

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