臺灣博碩士論文加值系統

由於選擇權契約的多樣化和複雜化加深了評價上的困難，本文使用一個在國內較少為人探討的方法—半徑基底函數內插(Radial Basic Function , RBF)，來對選擇權進行評價。我們採用以multiquadric為基底函數的MQ-RBF方法，藉由使用二項樹模型來選取計算的股價空間範圍與數值迭代上的修正來改進MQ-RBF的評價結果。經修正的計算區間服從股價的隨機過程和機率分佈，且方便RBF在評價上的操作。根據數值結果顯示，MQ-RBF的評價發現不論是歐式賣權或是美式賣權皆有相當精確的評價結果，相較於先前的研究有著大幅度的改善，且修正後的MQ-RBF在價平時可使精確度大幅的提升。另外，相較於二項樹模型法，MQ-RBF法在股價空間的切割上較具彈性，在使用較少的切割點與迭代次數的狀況下即可產生相當近似的精確結果。
另外，先前研究皆只對歐式賣權在RBF上進行收斂性的探討，但在此我們分別針對歐式和美式賣權在分割點及迭代上的收斂性進行探討。結果發現歐式和美式賣權在較小的切割距離 皆可有相當精確的結果，且較小的切割距離 皆需使用較多的迭代次數方可求得其結果。但是增加迭代次數會使得歐式賣權的評價誤差上升，而美式賣權的評價誤差卻會下降。

In this paper, we valuate options of single asset by using radial basis function (RBF) approach, which is rarely known in Taiwan. We utilize binomial tree model to generate the computing domain and adjust the iteration to enhance the accuracy of pricing. The revised computing domain has several advantages. First, it respects to the lognormal distribution of stocks; therefore, the computing of RBF would be located at the reasonable region. Second, it can easily be operated and modified the changing of the volatility or maturity of options. According to our results, the evaluation of European and American options are improved well especially for at-the-money.
In addition, we also examined mesh scaling and the numbers of time iteration of both the European and American options. The characteristics of mesh scaling are the same as previous research; however, the numbers of time iteration have an opposite phenomenon. Compared with European options, the valuation of American options has to increase the numbers of time iteration to get the accurate outcome.

目 錄
第一章 緒論 1
第二章 文獻回顧 2
第三章 模型建立 5
第一節 RBF簡介 5
第二節 RBF在選擇權上的應用 7
一、 歐式選擇權 7
二、 美式選擇權 10
三、 希臘字母 10
第四章 數值方法與修正 12
第一節 股價空間的選取與邊界條件 12
第二節 數值計算方法 14
第五章 數值結果 17
一、 歐式選擇權 17
二、 美式選擇權 22
三、 希臘字母 22
第六章 結論 29
參考文獻 30

參考文獻
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