界限選擇權雖屬新奇選擇權的一種，但在國外卻已是交易頻繁的商品，而在國內則尚未有此一商品的交易發生。因此，為了能讓國內投資人與券商更了解此一商品，本研究便以界限選擇權為對象，針對其訂價與避險兩大主題進行研究，期能獲至有貢獻之結論。

在訂價方面，以二項評價模型對界限選擇權進行評價時，會產生鋸齒狀的收歛情況，對於精確評價界限選擇權造成極大的困擾。本研究對此問題提供一修正二項評價模型的方法，可以有效地消除評價時收歛不佳的現象。

在避險方面，本研究使用靜態避險法對其進行避險，並結合修正後之二項評價模型以建構在靜態避險法下所需之複製投資組合，此乃以往所未有之研究。在本文中所獲至之結果顯示，使用靜態避險法對界限選擇權進行避險所達成之避險效率實為在動態避險下所不能及；同時，隨著時間間隔的縮小，避險效率會隨之提高。此外，使用修正後之二項評價模型所建構之複製投資組合較以未修正之二項評價模型所建構之複製投資組合，在避險效率上會有較佳之表現。

第一章 緒論 1

第一節 研究背景 .1

第二節 研究動機與目的 1

第三節 研究架構與流程 2

第二章 界限選擇權之簡介及其應用 5

第一節 界限選擇權之簡介 5

第二節 界限選擇權之應用 7

第三章 文獻探討 14

第一節 選擇權訂價模式 14

第二節 界限選擇權之訂價 19

第三節 界限選擇權之避險 22

第四章 界限選擇權之訂價分析 23

第一節 二項評價模型之訂價法 23

第二節 對二項評價模型之修正 29

第三節 避險係數之分析 36

第五章 界限選擇權之避險分析 39

第一節 靜態避險法之介紹 39

第二節 避險效率之分析 43

第六章 結論與建議 62

第一節 結論 62

第二節 研究限制 63

第三節 後續研究建議 63

參考文獻 65

附錄：MATLAB程式 67

Barrier option is one of those exotic options, yet it has been frequently traded in the foreign options markets. In Taiwan, this commodity is still new to most of us. Consequently, for a better understand and probably the issuance of this commodity, this research focuses on the pricing and hedging of barrier options, hoping that the research can obtain contributive conclusions.

On pricing, when using CRR model as a pricing method for barrier options, there exists a situation which the convergence of the pricing is saw-toothed, contributing to the imprecise pricing results. This study provides a modification for the CRR model that can mitigate the saw-toothed convergence very effectively.

On hedging, this study uses static hedge as a hedging measure, combining with the modified CRR model, which has very been studied before. The results of this study tell that, using static hedge can reach a very accurate hedging results, which is not attainable using dynamic hedge. Also, the more the time spacing shrinks, the more exact the hedge is. Finally, using modified CRR model as a basis producing replicating portfolio under static hedge can have a better performance in hedging than that of using unmodified CRR model.

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