2009-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/711173摘要：相對於Broadie and Detemple (1996) 中使用constant exercise boundary來估計美式選擇權的價格，本計畫提出使用exponential exercise boundary來估計美式選擇權的價格。藉由exponential exercise boundary的假設，本計畫試著要得到比Broadie and Detemple (1996)較佳的美式選擇權下界與提前執行邊界。當有了較佳的美式選擇權下界，則可以得出一個較佳的提前執行邊界，之後並可以使用Kim (1990), Jacka (1991)與Carr, Jarrow, and Myneni (1992)所提出的premium integral方法來得到較佳的美式選擇權上界，進而得到一個較緊的美式選擇權價格的上下界範圍。在本計劃中，我們將會比較此新方法與文獻中所提出計算或估計美式選擇權價格之方法的計算時間與精準度，包括了Broadie and Detemple (1996)中的 constant-exercise-boundary method、Binomial Black and Scholes (BBS) method、the Binomial Black and Scholes method with Ritchdson extrapolation (BBSR)、Huang, Subrahmanyam, and Yu (1996)中的integral equation method、Ju (1998)中的multipiece-exponential-function method、Geske and Johnson (1984) 所提出的Bermudan-option-with-Ritchardson-extrapolation method與 Ibanez (2003)所提出融合 integral-equation method 與improved Ritchardson extrapolation method 的方法。<br> Abstract: In contrast to the constant exercise boundary assumed by Broadie and Detemple (1996), this project suggests using an exponential function to approximate the early exercise boundary for American options. Using the exponential exercise boundary, this project tries to obtain lower bounds for American option prices and the optimal exercise boundary which improve the bounds of Broadie and Detemple (1996). With the tight lower bound for the optimal exercise boundary, one can apply it to obtain a tight upper bound of the early exercise premium (and thus a tight upper bound of the price) for the American option using the premium integral of Kim (1990), Jacka (1991), and Carr, Jarrow, and Myneni (1992). In this project, the comparisons for computation time and accuracy will be conducted among this new exponential-exercise-boundary method, the constant-exercise-boundary method in Broadie and Detemple (1996), the Binomial Black and Scholes (BBS) method, the Binomial Black and Scholes method with Ritchdson extrapolation (BBSR), the integral equation method in Huang, Subrahmanyam, and Yu (1996), the multipiece-exponential-function method in Ju (1998), the Bermudan-option-with- Ritchardson-extrapolation method in Geske and Johnson (1984), and the integral-equation-with-improved-Ritchardson-extrapolation method in Ibanez (2003).美式選擇權評價選擇權上下界提早執行邊界American option pricingupper and lower bounds for optionsearly exercise boundary