控制變異數法在美式選擇權之應用

Abstract

自從Longstaff and Swartz (2001)提出的最小平方估計法 (least-squares Monte Carlo)，解決了蒙地卡羅模擬法難以用於美式選擇權之訂價的一大缺點。於是，蒙地卡羅模擬法簡單、易懂，且易於應用至多資產商品的特性，使得蒙地卡羅模擬廣泛地被用於選擇權的評價問題上。然而，蒙地卡羅模樣通常需要大量的模擬路徑，才能得到較好的估計；這使得評價變得極為耗時。 本研究即是探討兩種降低變異的方法，希望能藉此提昇蒙地卡羅的模擬效率。這兩種降低變異的方法分別是由Rasmussen (2005)以及Duan and Simonato (2001)所提出來的。本研究將之分別應用到美式賣權及極大值買權的評價，結果發現由Rasmussen (2005)所提出來的方法，皆能有效地降低模擬的變異程度。

For many complex options, analytical solutions are not available. In these cases a Monte Carlo simulation is computationally inefficient, the variance reduction method can be used to improve the efficiency of a Monte Carlo simulation. In this thesis we apply the two variance reduction methods proposed by Rasmussen (2005) and Duan and Simonato (1998) in American option pricing. We find that the variance reduction method proposed by Rasmussen can provide significant improvement of efficiency than Duan and Simonato even the combination of these two methods does not perform better than only using the variance reduction methods proposed by Rasmussen. We also apply this variance reduction method proposed by Rasmussen in the valuation of two-, three- or five max-call options and we find that they can provide significant improvement both on efficiency and accuracy for pricing.