臺灣博碩士論文加值系統

Heston 的隨機波動度模型不僅放寬了 Black-Scholes 的固定波動度假設，使得其可以更貼近實證資料，如報酬厚尾分佈(fat return tail)、波動的群聚現象(volatility clustering)等，另外也有著方便計算的歐式選擇權封閉解。但在美式選擇權的情況便複雜許多，因為其牽涉到履約曲面的計算，本篇論文延伸 Chiarella and Ziogas (2005) 之訂價方法，採用近似履約曲面並結合數值積分方式訂價選擇權，可以在十分有效率的情況下計算選擇權價格，快速幫助判斷是否需要履約。

Heston''s model not only relaxes Black-Scholes''s fixed volatility assumptions, but also reflects empirical situations, such as fat return tails, volatility clustering, etc. Moreover, Heston''s models provides closed solution to European option that is easy to calculate. However, calculating American options is much more complicated since it involves calculating the exercise surface. This research extends the pricing method of Chiarella and Ziogas (2005) by approximating exercise surfaces with numerical integration, which significantly improves pricing efficiency.

口試委員會審書 #
誌謝 i
摘要 ii
Abstract iii
第一章 概述 1
第二章 模型假設與訂價問題 3
第三章 近似履約曲面 6
第四章 數值結果與分析 9
4.1履約曲面差異 10
4.2低波動度 11
4.3中波動度 11
4.4高波動度 12
4.5數值結果小結 12
第五章 結論 14
參考文獻 15
表1、低波動度下選擇權價格 18
表2、低波動度下誤差及計算時間 20
表3、中波動度下之選擇權價格 21
表4、中波動度下之誤差及計算時間 23
表5、高波動度下選擇權價格 24
表6、高波動度下之誤差及計算時間 26
表7、全部資料下之誤差及計算時間 27

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