American Barrier Option

美式障礙選擇權是依照過去股價是否碰觸障礙價格，來衡量此選
擇權是否失效或生效。在Black-Scholes 的假設之下，我們利用Feynamn-Kac的方法推導美式選擇權的評價公式，並且更進一步推倒各種美式障礙選擇權的評價公式。因為美式選擇權與美式障礙選擇權的提早履約邊界有所不同，故可以推出美式障礙選擇權的in-out parity不存在。

An American barrier option is an option contract in which the option holder receives an American option or becomes nullified conditional on the underlying stock price touching a barrier level. We use the Feynamn-Kac method to value American options and present analytic valuation formulas for American under the Black-Scholes pricing framework. Because the early exercise boundary of the American barrier option is different from the early exercise boundary of the vanilla American option, we claim the in-out parity does not hold.