本研究採用邊界積分法以精確的積分表現式解決具有邊界條件之Black-Scholes Model偏微分方程，利用格林函數(Green’s function)搭配邊界積分法以求得精確數值解。現今學術界已有許多與障礙選擇權評價相關之研究，此商品特點為設有障礙價格，而資產是否易觸及障礙價格將影響投資人的獲利或損失，在此以風險控管角度探討障礙選擇權觸及邊界障礙之機率，並透過各種參數討論其對機率與期望值變化之影響，數值例以台灣上市上櫃永續價值指數為例，望可提供投資人作為參考依據之一。

In this study, the boundary integral method is used to solve the Black-Scholes Model partial differential equation with boundary conditions and the Green’s function is used with the boundary integral method to obtain the exact numerical solution. Nowadays, there have been many studies related to the evaluation of barrier options. The barrier options are characterized by a predetermined price or barrier and whether the underlying asset price is easy to hit the boundary condition will affect the investors’ profit or loss. We will discuss the hitting probability of barrier options, then discuss its impact on the probability and the expected value change through various parameters. The Taiwan sustainability index as an example. Hoping to provide investors with some reference through this paper.

壹、緒論 1
一、研究動機與背景 1
二、研究目的與預期成果 3
三、研究流程 4
貳、文獻探討 5
一、選擇權基本介紹 5
二、障礙選擇權簡介 8
三、障礙選擇權相關文獻 9
四、企業永續經營相關文獻 12
參、數值方法 17
肆、數值例 21
一、敏感度分析 22
二、期望值 44
伍、結論與建議 55
參考文獻 57

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