美式障礙選擇權

American Barrier Option

蔡承文(Cheng-Wen Tsai)

指導教授 ： 彭栢堅

國立臺灣大學/理學院/數學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.00639

摘要

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。

關鍵字

美式選擇權 ； 美式障礙選擇權

並列摘要

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.

並列關鍵字

American Option ； American Barrier Option

參考文獻

[1] AitSahlia,F.,L.Imhof,and T.L.Lai.[2003]: Fast and Accurate Valuation of American Barrier Options. Journal of Computational Finance, vol.7,pp.129-145.

[2] AitSahlia,F.,L.Imhof,and T.L.Lai.[2004]: Pricing and Hedging of American Knock-In Option. The Journal of Derivatives,Spring,44-50.

[4] Boyle, P., Lau, S.H.,[1994].: Bumping up against the barrier with the binomial method. Journal of Derivatives 2,6-14.

[5] Cheuk, T.H.F., Vorst, T.C.F.,[1996].: Complex barrier options. Journal of Derivatives 4, 8-22.

[7] Geman, H.&M.Yor,[1996]: Pricing and Hedging double barrier options: A probabilistic approach, Mathematical Finance 6,365-378.