文獻上有學者提出數種利用蒙地卡羅模擬來評價美式選擇權的方法，其中
Barraquand-Martineau（BM,1995）將資產價格之空間予以分隔，並觀察每
條路徑在不同區域間移動的機率，再以類似二項式的方式回推加以求解。
Raymar-Zwecher（RZ,1997）則是修正BM的模型，將資產價格之空間分隔
成兩個維度，然後同樣觀察每條路徑在不同區域間移動的機率，再以類似
二項式的方式回推來加以求解。在本文中，我們主要是發現BM及RZ兩美
式選擇權定價模型對於持有價值的估計有所偏誤，並進一步提出改進之道
，建構修正模型，並將修正模型應用於美式標準買權、美式下終賣權、美
式回顧賣權、美式幾何平均價格買權、美式算術平均價格買權以及美式最
大值買權共六種美式選擇權評價之上，針對不同的區塊分隔方式以及不同
的區塊分隔因子加以探討，並以最近文獻上的估計值作為比較基準，檢視
修正模型是否適用於這六種美式選擇權的評價。最後，我們亦利用相反變
異法（Antithetic Variate Approach）、動差配適模擬法（Moment Matching
Simulation）以及平賭過程配適模擬法（Empirical Martingale Simulation）三
種降低變異方法，檢驗其對於上述六種歐式以及美式選擇權的適用性。
由本文之研究分析我們得到下列幾點結論：（1）、修正模型相較於BM模
型或RZ模型而言，的確可以改善對於持有價值估計的準確性，進而增加對
於美式選擇權價值估計的準確程度；（2）、根據選擇權的特性選擇不同
的區塊分隔方式以及不同的區塊分隔因子是相當重要的，因為這會影響到
估計值的準確程度和收斂速度；（3）、修正模型對於六種美式選擇權評
價均有不錯的效果，且對於價外或價內的選擇權，準確度較價平選擇權來
得高；（4）三種降低變異方法中，大致上以平賭過程配適模擬法的效果最
好，動差配適模擬法次之，相反變異法較差，不過均較原始蒙地卡羅模擬
的標準差有顯著改善，且對於越是價內的選擇權，改善的程度越顯著。

參考文獻
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1.廖志峰，保本基金之設計與評價，中央大學財務管理研究所碩士論文，
民國88年6月。
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