彭栢堅臺灣大學：數學研究所蔡承文Tsai, Cheng-WenCheng-WenTsai2007-11-282018-06-282007-11-282018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/59475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.Contents ii Acknowledgements v Abstract in Chinese vi Abstract vii I.INTRODUCTION 1 II. DECOMPOSITION FORMULAS FOR AMERICAN OPTION 6 III. AMERICAN DOWN-OUT CALLS AND UP-OUT PUTS 12 3.1 Early exercise boundary for American down-out calls, up-out puts 12 3.2 Decomposition Formula for American down-out calls, up-out puts 16 3.3 The possibility of early exercise for American down-out call when there is no dividend 27 IV. AMERICAN DOWN-IN CALLS AND UP-IN PUTS 33 4.1 Decomposition Formula for American down-in calls, up-in puts 33 4.2 In-out barrier parity relation for American barrier options 43 V. CONCLUSION 50 Appendix 51 References 53632041 bytesapplication/pdfen-US美式選擇權美式障礙選擇權American OptionAmerican Barrier Optionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59475/1/ntu-95-R92221009-1.pdf