對於回顧型選擇權的評價，本篇研究是利用Cheuk and Vorst (1997)的轉換計價單位方法結合 Ritchken and Trevor (1999)多元樹模型的架構建立一個評價回顧型選擇權的單一狀態變數之多元樹模型。在連續觀察時間情況下能夠快速且精確地逼近Conze and Viswanathan (1991)推導的回顧型選擇權封閉解，而在離散觀察時間情況下能夠得到正確的評價結果並與Heynen and Kat (1995)推導的離散回顧型選擇權之數值解比較。
本研究之評價模型在評價連續歐式浮動履約價回顧型買權時，隨著多元樹的分枝數及切割期數的逐漸增加，雖然能夠在計算效率有較佳的表現，但是在封閉解的逼近上，仍然存在小數點第二位的誤差。而在離散歐式浮動履約價回顧型買權的評價上，當回顧型選擇權的觀察期數越頻繁，越能夠凸顯此縮減式多元樹評價模型的準確性及快速性，不僅能夠快速逼近Monte Carlo的模擬值，而且評價結果皆能在95%的信賴區間，另外亦能夠在計算效率上領先Heynen and Kat(1995)所提出的離散回顧型選擇權評價方法，可見此縮減式多元樹的評價模型能夠是更能夠與現實中的股價波動情形相符合。

For the valuation of lookback option, this study intends to establish an one-state variable multinomial lattices model to evaluate lookback option based on the notions of changing numeraire in Cheuk and Vorst (1997) and the tree model in Ritchken and Trevor (1999). With the framework of one-state variable multinomial lattices model, the results of continues-sampled lookback option prices can converge to efficiently the closed-form solution derived by Conze and Viswanathan (1991). The results of discrete-sampled lookback option prices can correctly approach the results of the Monte Carlo estimation and the closed-form solution derived by Heynen and Kat (1995).
For the valuation of the continues-sampled lookback options, this model can generate more accurate results with the increase of number of multinomial lattices’ branches and the number of time steps, but there is still small bias between our results and the closed-form solution. For the valuation of the discrete-sampled lookback options, the more frequently is the observation number, this model can obtain correct result more fast and accurately. The results with one-state variable multinomial lattices model can not only approach the results of Monte Carlo estimation fast, but also are always within 95% confidence interval. In addition, this model can have better efficiency than the numerical implementation of the closed-form solution in Heynen and Kat (1995) for pricing discrete-sampled lookback options. Consequently, one-state variable multinomial lattices model of this study can generate more accurate results in real life.

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