本文首先討論界限選擇權的評價方法，透過計算界限條件於特定時間生效的機率，配合風險中立評價的概念，導出計算界限選擇權期初價值的公式，我們所得到的結果是一封閉解的形式，透過此一公式我們不需要討論標的資產價格走勢的樹狀圖，即可由期初的相關參數求出界限選擇權的價值。我們除了以特定數值實際操作，更進一步比較該評價公式與傳統選擇權的二項式評價公式之間的關係，結果顯示兩種評價模型所得到的結果完全相同。其次我們以界限選擇權的評價方式討論國安基金的價值，除了導出計算國安基金價值的公式，並進一步利用導出的評價公式，分析國安基金對市場的影響，結果顯示當事件不會改變市場基本面的表現時，國安基金進場護盤能夠讓股市止跌回升，以及降低股市波動性。最後我們以導出的國安基金評價公式，實際計算歷次國安基金進場護盤時的價值，並對照國安基金實際護盤結果，結果顯示本文的模型能夠估計國安基金的衍生價值，並且能夠預測國安基金的護盤門檻以及護盤價位。除此之外，本文的評價方式還可以應用於例如公司的破產成本、代理成本，以及像台灣股市的漲跌停限制、芝加哥期貨交易所的賣權限價等等，另外目前許多公司募集資金常會採用的或有負債，其行為模式與界限選擇權的概念類似，因此也都可以界限選擇權評價公式來評估其價值或影響。我們希望本文的界限選擇權評價公式以及其推導過程，能夠有助於解決前面所提及的問題，甚至於其他更多相關的課題。

In the first part of this article, we discuss the time and the probability for the barrier option to become effective, and then employ the risk neutral assumption to derive the pricing formula of the barrier option. Our pricing formula is a closed form solution, and we may calculate the price of the barrier option without considering the Binomial tree of the underlying asset. We also calculate the traditional option price by our pricing formula, and compare the result to the value that is calculated by Binomial pricing formula. Both of them give the same value about the tradition option, and thus we may regard the tradition option as the special case of the barrier option. In the second part of this article, we employ the pricing formula of the barrier to derive the value of the National Finance Stabilization Fund, and then analyze the impact of the NFSF to the market. Our results reveal that when the benchmark market is not shifted by the bad news, then the NFSF may advance and stabilize the stock price index. In fact, many new style derivatives have the characteristics like barrier option, for example, a convertible bond with forced convert clause, which is a up-and-out call. Other course like bankruptcy costs, agency problems, and contingent liabilities etc, which can all be solved by the pricing formula in our discussion. We hope that results and the process in this article are helpful in solving above questions.

目 錄
摘要………………………………………………………………………………3
壹、 導論…………………………………………………………………………5
貳、 文獻探討……………………………………………………………9
參、 界限選擇權的評價公式……………………………………………………12
一、 界限生效的時間與機率…………………………………………12
二、 界限選擇權的價值………………………………………………16
三、 二項式解與Hull-White封閉解的比較……………………………28
四、 結論與應用………………………………………………………29
肆、 國安基金評價公式…………………………………………………………31
一、 模型設定…………………………………………………………32
二、 授權以後國安基金的價值………………………………………34
(一) 國安基金價值的產生過程……………………………………………….34
(二) 國安基金價值的計算…………………………………………………….36
(三) 比較靜態分析…………………………………………………………….38
(四) 策略意涵………………………………………………………………….41
三、 授權以前的國安基金價值………………………………………42
四、 國安基金對股價指數波動性的影響……………………………45
五、 國安基金護盤實例………………………………………………49
六、 歷次授權下的國安基金衍生價值…………………………………..57
伍、 結論…………………………………………………………………………64
附錄………………………………………………………………………………66
參考文獻…………………………………………………………………………69

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