呂育道臺灣大學：資訊工程學研究所劉俊洋Liu, Chun-YangChun-YangLiu2007-11-262018-07-052007-11-262018-07-052005http://ntur.lib.ntu.edu.tw//handle/246246/54004GARCH模型非常適用於描述資產價格在時間上的波動度。然而，使用樹這類的演算法來評價GARCH選擇權卻會遭遇到程式執行時間呈指數成長、評價後的價格不精確等等問題。Ritchken和Trevor在1999年以及Cakici和Topyan在2000年分別提出過三元樹的演算法來評價GARCH模型選擇權，不過當切割期數超過某一門檻後，此三元樹將會指數成長導致無法得到正確價格。Lyuu和Wu在2003年針對前兩個三元樹演算法提出改良的版本，用來解決上面遭遇的問題。不過這個改良的演算法仍然存在些問題，當切割期數漸增時，計算出的選擇權價格會有個向下遞減的趨勢。在這篇論文中，我們將提出一個方法來解決上述的問題，並利用計算出的數值結果來印證我們方法的具有效率和其正確性。The GARCH model has been successful in describing the volatility dynamics of asset return series. However, tree-based GARCH option pricing algorithms suffer from exponential running time, inaccuracy, or other problems. Lyuu and Wu proved that the trinomial-tree option pricing algorithms of Ritchken and Trevor (1999) and Cakici and Topyan (2000) explode exponentially when the number of partitions per day, n, exceeds a threshold determined by the GARCH parameters. The improved algorithm of Lyuu and Wu (2003) still contains some problems. For example, the option prices suffer a trend to deviate from true values as n increases. This thesis proposes a new methodology to further improve the Lyuu-Wu algorithm by addressing this problem. We will confirm our algorithm's efficiency and accuracy with numerical experiments.1 Introduction 4 2 The GARCH Model 7 3 The RTCT Tree 8 4 Interpolated Volatilities and Backward Induction 14 5 The Mean-Tracking (MT) Tree 17 5.1 Volatility Interpolation Schemes . 17 5.2 Tree Building . . . . . . . . . . .18 5.3 Backward Induction . . . . . . . . 21 6 Comparison between MT-LL, MT-C and RTCT 23 7 Conclusions 25236321 bytesapplication/pdfen-USGARCH模型三元樹選擇權評價三元內插法GARCH modeltrinomial treeoption pricingcubic interpolationthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54004/1/ntu-94-R92922123-1.pdf