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| 研究生： |
朱苡榕 Zhu, Yi Rong |
|---|---|
| 論文名稱： |
GARCH-Lévy匯率選擇權評價模型 與實證分析 Pricing Model and Empirical Analysis of Currency Option under GARCH-Lévy processes |
| 指導教授： |
林士貴
Lin, Shih Kuei 蔡紋琦 Tsai, Wen Chi |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2016 |
| 畢業學年度： | 104 |
| 語文別： | 中文 |
| 論文頁數： | 49 |
| 中文關鍵詞： | 匯率選擇權評價 、GARCH 、Lévy過程 、跳躍風險 、波動聚集 |
| 外文關鍵詞： | Currency option pricing formula, GARCH, Lévy-process, Jump risk, Volatility clustering |
| 相關次數： | 點閱：59 下載：16 |
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本研究利用GARCH動態過程的優點捕捉匯率報酬率之異質變異與波動度叢聚性質，並以GARCH動態過程為基礎，考慮跳躍風險服從Lévy過程，再利用特徵函數與快速傅立葉轉換方法推導出GARCH-Lévy動態過程下的歐式匯率選擇權解析解。以日圓兌換美元(JPY/USD)之歐式匯率選擇權為實證資料，比較基準GARCH選擇權評價模型與GARCH-Lévy選擇權評價模型對市場真實價格的配適效果與預測能力。實證結果顯示，考慮跳躍風險為無限活躍之Lévy過程，即GARCH-VG與GARCH-NIG匯率選擇權評價模型，不論是樣本內的評價誤差或是在樣本外的避險誤差皆勝於考慮跳躍風險為有限活躍Lévy過程的GARCH-MJ匯率選擇權評價模型。整體而言，本研究發現進行匯率選擇權之評價時，GARCH-NIG匯率選擇權評價模型有較小的樣本內及樣本外評價誤差。
In this thesis, we make use of GARCH dynamic to capture volatility clustering and heteroskedasticity in exchange rate. We consider a jump risk which follows Lévy process based on GARCH model. Furthermore, we use characteristic function and fast fourier transform to derive the currency option pricing formula under GARCH-Lévy process. We collect the JPY/USD exchange rate data for our empirical analysis and then compare the goodness of fit and prediction performance between GARCH benchmark and GARCH-Lévy currency option pricing model. The empirical results show that either in-sample pricing error or out-of-sample hedging performance, the infinite-activity Lévy process, GARCH-VG and GARCH-NIG option pricing model is better than finite-activity Lévy process, GARCH-MJ option pricing model. Overall, we find using GARCH-NIG currency option pricing model can achieve the lower in-sample and out-of sample pricing error.
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
第二章 文獻回顧 4
2.1 匯率選擇權評價模型 4
2.2 隨機波動度選擇權評價 5
2.3 GARCH 選擇權評價 6
第三章 GARCH-Lévy 匯率選擇權評價模型 9
3.1 報酬率與 Lévy 跳躍風險模型 9
3.2 GARCH 動態過程 14
3.3 測度轉換 16
3.4 匯率選擇權評價公式 19
3.5 參數估計方法 21
第四章 實證分析 23
4.1 匯率選擇權資料描述 23
4.2 匯率報酬率與匯率選擇權之敘述統計 25
4.3 模擬分析 27
4.4 模型評價表現 27
第五章 結論 29
參考文獻 30
附錄
附錄 A：測度轉換 32
附錄 B：特徵函數推導 37
附錄 C：匯率選擇權評價公式推導 42
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