臺灣博碩士論文加值系統

選擇權是一種常見的衍生性金融商品，在世界各地的金融市場交易非常活躍。也因應不同的客戶需求，進而衍生出各種不同交易方式的選擇權，亞式選擇權就是其中之一。亞式選擇權評價需計算未來資產價格之平均，使得亞式選擇權沒有封閉解。
　　許多資產價格報酬變動無法完全用幾何布朗運動解釋，若是出現重大新聞，資產價格即會急遽波動，Merton(1976)提出跳躍擴散模型解釋此現象。
　　本研究以股價變動符合跳躍擴散模型為基礎，導出亞式遠期生效選擇權解析近似公式，以蒙地卡羅法模擬的亞式選擇權為基準，判斷解析近似公式之準確度。

Options is a common financial derivatives products, and the transactions of options are active around the world. In response to different customers needs, and then derives a variety of different types of options, one of them is Asian options. It does not exist closed form for Arithmetic Asian options because the payoff of Asian options is determined by the average underlying price over some pre-set period of time.
Changes in asset prices can not be explained entirely by geometric Brownian motions. Asset prices will fluctuate sharply if significant events occur. Jump-diffusion model proposed by Merton(1976) is explained this phenomenon.
In this study we derive analytic approximation formulae for pricing strike Asian options contain Jump-diffusion model. We use Monte Carlo simulation approach as benchmark verifying the accuracy of our formulae.

目錄
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 4
第三節 論文架構及研究步驟 4
第二章 文獻回顧 6
第一節 Bouaziz, Briys and Crouhy(1994)模型 6
一、初始時間t在T-A前 7
二、初始時間t在T-A後 9
第二節　Tsao, Chang and Lin(2003)模型 10
一、初始時間t在T-A前 11
二、初始時間t在T-A後 12
第三章 研究方法 15
第一節 結合Bouaziz, Briys and Crouhy (1994)模型 16
一、 初始時間t在T-A之前 16
二、 初始時間t在T-A之後 18
第四章 研究結果與分析 21
第五章 結論與未來研究方向 31
參考文獻 33
附錄A 37
A.1 定理3.1.1證明 37
A.2 定理3.1.2證明 45
附錄B 49



圖目錄
圖 1　研究流程圖 5
圖 2 初始時間t在T-A前時間軸 16
圖 3 初始時間t在T-A後時間軸 19
圖 4 在[0,A]時間跳躍示意圖 38

 
表目錄
表 1　各亞式選擇權評價模型效用比較 25
表 2　各亞式選擇權評價模型效用比較 26
表 3　各亞式選擇權評價模型效用比較 27
表 4　各亞式選擇權評價模型效用比較 28
表 5　各亞式選擇權評價模型效用比較 29
表 6　各亞式選擇權評價模型效用比較 30

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