臺灣博碩士論文加值系統

在過去，Black-Sholes(1973)模型已是一個選擇權定價模型的基礎，但對於深價內、深價外的選擇權則常有定價錯誤（mispricing）的情況，因此，有許多文獻提出不同的選擇權定價模型來調整克服；另一方面，風險值（VaR）亦已成為執行風險管理的重要工具之一，在學術界也發表了許多關於此範疇之研究文獻。但目前鮮少有結合兩者範疇去做探討之相關研究。因此，為能更深入了解兩者範疇之關係，故選以台灣加權指數（TAIEX）為題材，進行用選擇權所得出的隱含指數價格與風險值之相關研究。
本研究從台灣加權指數出發，透過參考Jarrow and Rudd(1982)文獻所提出的選擇權定價模型來做調整及克服布雷克─休斯模型，進行台灣加權指數的隱含機率分配之取得，並搭配歷史資料價格來算出VaR進行比較。我們發現利用Jarrow and Rudd(1982)文獻所提出的選擇權定價模型去做風險管理，相較於花時間去看財務報表或公開資訊等資料時，將會是一個很好且簡單易執行的參考依據。

In the past, the Black-Sholes model, studied by Black-Scholes(1973), was the basis for an option pricing model, but it frequently misprices deep in-the-money and deep out-of-the-money options. Hence, a lot of literature proposed different model designed to overcome most of its limitations. On the other hand, value at risk（VaR）has become one of the most important tools for risk management, and many research papers have been published in the academic field. But there is little the relevant research to explore between the two field. Therefore, in order to gain a deeper understanding of the relationship between the two categories, we choose the Taiwan Stock Exchange（TAIEX）as the theme, and use the option to obtain the implied stock price index and compute the corresponding VaR to do the related research.
Based on the selection pricing model proposed by Jarrow and Rudd(1982), this study uses the adjusted model to overcome the Black-Sholes model, and then gets the implied probability distribution of TAIEX with using the historical data prices to calculate VaR to compare. We find that using the option pricing model proposed by Jarrow and Rudd(1982)to do risk management, it would be a better reference and easier to implement than the thing that taking time to look at financial statements or public information.

目錄
中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
圖目錄 vi
表目錄 vii
一、緒論 1
1-1研究背景與動機 1
1-2研究目的與問題 2
1-3研究流程 3
二、文獻探討 4
2-1選擇權定價模型 4
2-2風險值 6
三、研究方法 8
3-1 Jarrow and Rudd(1982)的模型 8
3-2資料選取 9
3-3估計隱含動差 10
四、資料分析 12
4-1選擇權的定價模型與風險值之間的關係 12
4-2偏態與峰態的延伸探討 26
五、結論與建議 35
5-1研究結論 35
5-2未來研究建議 36
參考文獻 37
附錄一：Jarrow and Rudd(1982)的模型推導 39
附錄二：Matlab程式碼 46
1.估計Jarrow and Rudd(1982)模型之隱含偏態、峰態 46
2.利用蒙地卡羅模擬估計股價走勢 48

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