本篇論文是結合Longstaff and Schwartz (2001) 提出的最小平方法與Huge and Rom-Poulsen (2004) 提出降低變異數 (variance reduction) 的技巧來評價美式選擇權。Longstaff and Schwartz (2001) 使用最小平方法估計美式選擇權的持有價值，Huge and Rom-Poulsen (2004) 則是利用最小平方法計算標的資產的價格。當標的資產須用蒙地卡羅的方式模擬時，計算選擇權的報酬會產生偏誤的現象。我們應用這個演算法分別去估計標的資產為債券的障礙選擇權 (barrier option) 與重設選擇權 (reset option) 的價格，並且以數值模擬的結果呈現出降低變異數的效果。 This paper develops an algorithm that combines the Longstaff and Schwartz (2001) simulation algorithm and the variance reduction technique proposed in Huge and Rom-Poulsen (2004) to simulate American-style option prices on securities such that their prices can be found by the Monte Carlo simulations. Longstaff and Schwartz (2001) used the least squares method to estimate the optimal exercise boundary of American options, Huge and Rom-Poulsen (2004) used the same method to calculate the price of underlying security. In this paper, we apply this algorithm to value various options, such as barrier option and reset option. Bias reduction is also involved in algorithm, since we know that using simulated prices of the underlying security to compute option payoff causes an upward bias in option prices. We use numerical results to show that this algorithm can provide significant improvement on efficiency and accuracy for pricing barrier bond option and reset bond option.
