臺灣大學: 資訊網路與多媒體研究所呂育道鄒志鴻Chou, Chih-HungChih-HungChou2013-03-222018-07-052013-03-222018-07-052010http://ntur.lib.ntu.edu.tw//handle/246246/251436障礙選擇權是一種路徑相依的衍生性金融產品，其價格決定於資產價格是否碰觸到給定的障礙H。一般而言，在許多評價樹模型中，分配誤差與非線性誤差會導致評價結果無法平滑收斂。本論文進一步探討障礙H(t)與資產年化波動率sigma(t)為時變的函數，以符合實際的市場條件。然而這會導致在傳統的評價樹模型中遭遇困難。首先，隨時間變動的障礙H(t)會造成障礙沒有落在評價樹的節點上，而使非線性誤差更大。而隨時間波動的資產年化波動率sigma(t)會使評價樹每一期的分支無法接合，並使計算複雜度呈指數成長。 Amin（1991）提出的二元樹模型可允許標的物資產年化波動率為隨時間變動的函數，並能以O(n^2)的計算複雜度評價陽春選擇權。Dai and Lyuu（2008, 2010）所提出的bino-trinomial tree模型可藉由調整評價樹的結構，大幅降低非線性誤差並快速而精確地評價多種金融產品。 在本篇論文中，我們延伸應用了Dai and Lyuu（2008, 2010）提出的bino-trinomial tree模型與Amin（1991）的模型，用來評價時變波動率與非線性障礙邊界下的選擇權價格。我們以蒙地卡羅模擬驗證了我們評價模型的正確性：在計算複雜度O(n^2)下做出精確的評價。同時，數值結果顯示計算出的選擇權價格能夠快速與平滑地收斂，而不會產生巨幅震盪。Barrier options are path-dependent options whose payoff depends on whether the underlying asset''s price reaches or exceeds a given barrier H. In many numerical methods, the distribution error and the nonlinearity error together make the pricing results converge slowly or even oscillate significantly. This thesis incorporates the time-varying barrier H(t) and volatility sigma(t) into the pricing model to reflect the markets better. However, it would be more difficult to price a barrier option accurately by traditional tree models. First, that the nodes in the tree cannot be made to coincide with the time-varying barrier will magnify the nonlinearity error. Furthermore, working with a time-varying volatility sigma(t) that is consistent with the market would make the tree model uncombined and grow exponentially, unless deliberate efforts are given to modify the traditional tree models. Amin (1991) proposed a binomial tree model to price vanilla options under time-varying volatility. Its time complexity is O(n^2). Dai and Lyuu (2008, 2010) developed the bino-trinomial tree model (BTT) which reduces the nonlinearity error sharply by adjusting its structure for pricing a wide range of derivatives accurately and efficiently. In this thesis, we extend Dai and Lyuu’s BTT model (2008, 2010) by combining the method in Amin (1991) to compute accurate estimates of single-barrier option price with a time-varying volatility and an exponential barrier. The proposed pricing model is verified with Monte Carlo simulation, and it achieves accurate results with O(n^2) time. Furthermore, the prices converge smoothly and quickly.1113784 bytesapplication/pdfen-US障礙選擇權時變波動率非線性障礙樹模型非線性誤差barrier optiontime-varying volatilitynon-linear barriertree modelnonlinearity errorhttp://ntur.lib.ntu.edu.tw/bitstream/246246/251436/1/ntu-99-R97944012-1.pdf