本研究首先將Hull-White(1993) 所提出之美式標準型向後看選擇權之訂價方法 ，擴展至 Conze-Viswanathan (1991) 所定義之其他三種向後看選擇權之上，然後我們以模 擬的方式檢驗 Hull-White (1993) 效率訂價法之收歛速度， 由模擬結果發現 Hull-White (1993) 效率訂價法之收歛速度非常緩慢， 因此限制了該模型之實用價值， 為了解決 Hull-White (1993) 效率訂價法收歛速度緩慢的缺失， 我們引用 Hull-White (1998) 之控 制變數技術 (Control Variate Technique )， 並利用 Conze-Viswanathan (1991) 所導出 之封閉式解為控制變數，進而發展出一個快速收歛之美式向後看選擇權訂價法。由模擬結果 得知，本文所提出之修正型 Hull-White 美式向後看選擇權訂價法，不但可以準確地計算出 各式各樣的美式向後看選擇權價格， 且其計算效率亦較原 Hull-White (1993) 效率定價法 快了近 600 至 900 倍。 再則，我們亦將 Conze -Viswanathan (1991) 所導致之封閉式解 加以偏微分，以求得歐式向後看選擇權之各種避險比率，並進而以這些避險比率作為控制變 數，快速且準確地計算出各式各樣的美式向後看選擇權避險比率。

　　　　　This study firstly extends the Hull and White (1993) efficient procedures for valuing American-Style lookback options to other three types of lookback options defined by Conze and Viswanathan (1991). We then test the convergence speed of the Hull and White (1993) model by carrying out simulations. From the simulation results, we find that the convergence speed of the Hull and White (1993) model is very slow. The shortcoming of slow convergence limits the applications of the Hull and White (1993) model into practice. To solve the shortcoming of slow convergence encountered in the Hull and White (1993), we employ the closed-from solution of European lookback options derived by Conze and Viswanathan (1991) as a control variable to construct a fast convergence model for valuing various American-Style lookback options. From the simulation results, the modified Hull-White model is not only 600 to 900 times faster than the Hull and White (1993) model but also able to compute the option values and Hedge ratios in a high degree of accuracy.