臺灣博碩士論文加值系統

本文在Kamrad and Ritchken(1991)提出的具有拓展參數 λ (≥1) (stretch parameter) 的三元樹模型基礎上，對於多項式障礙選擇權(polynomial barrier option)使用組合數學方法(combinatorial approach)開發計算複雜度為O(Dn)的評價算法，完成數學上的證明，以及數值結果的驗證。與傳統的計算複雜度為O(n^2+Dn)的backward induction方法相比，表現出較高的效率。

This thesis uses combinatorial approach to develop O(Dn) time complexity algorithm for polynomial barrier option based on the trinomial lattice model with a stretch parameter which was developped by Kamrad and Ritchken. We demonstrate the time complexity of the new algorithm is O(Dn) from the aspects of mathematics and numerical results. Especially, the numerical results show our algorithm is superior to the traditional backward induction approach in terms of efficiency.

摘要 I
ABSTRACT II
誌謝 III
目錄 VI
表目錄 VIII
圖目錄 IX
一、緒論 1
第一節 研究動機和背景 1
第二節 研究目的 2
第三節 研究架構 3
二、文獻回顧 5
三、研究方法 8
第一節 Kamrad and Ritchken模型 8
第二節 多項式選擇權(polynomial option) 10
第三節 組合式算法原理 11
第四節 反射原理 12
第五節 評價多項式障礙選擇權(polynomial barrier option) 14
第六節 用於選擇權求和公式的線性時間算法 30
第七節 多項式障礙選擇權的組合數學評價方法 37
四、數值分析和結論 46
參考文獻 61

參考文獻
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