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| 研究生： |
連育民 Lian, Yu Min |
|---|---|
| 論文名稱： |
狀態相依跳躍風險與美式選擇權評價：黃金期貨市場之實證研究 State-dependent jump risks and American option pricing: an empirical study of the gold futures market |
| 指導教授： |
廖四郎
Liao, Szu Lang |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
商學院 - 金融學系 Department of Money and Banking |
| 論文出版年： | 2014 |
| 畢業學年度： | 102 |
| 語文別： | 英文 |
| 論文頁數： | 51 |
| 中文關鍵詞： | 美式黃金期貨選擇權 、狀態轉換跳躍擴散過程 、Merton測度 、Esscher轉換 、最小平方蒙地卡羅法 |
| 外文關鍵詞： | American gold futures option, Regime-switching jump-diffusion process, Merton measure, Esscher transform, Least-squares Monte Carlo method |
| 相關次數： | 點閱：345 下載：11 |
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本文實證探討黃金期貨報酬率的特性並在標的黃金期貨價格遵循狀態轉換跳躍擴散過程時實現美式選擇權之評價。在這樣的動態過程下，跳躍事件被一個複合普瓦松過程與對數常態跳躍振幅所描述，以及狀態轉換到達強度是由一個其狀態代表經濟狀態的隱藏馬可夫鏈所捕捉。考量不同的跳躍風險假設，我們使用Merton測度與Esscher轉換推導出在一個不完全市場設定下的風險中立黃金期貨價格動態過程。為了達到所需的精確度，最小平方蒙地卡羅法被用來近似美式黃金期貨選擇權的價值。基於實際市場資料，我們提供實證與數值結果來說明這個動態模型的優點。
This dissertation empirically investigates the characteristics of gold futures returns and achieves the valuation of American-style options when the underlying gold futures price follows a regime-switching jump-diffusion process. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the advantages of this dynamic model.
中文摘要 I
Abstract II
Acknowledgements III
Contents IV
List of Tables VI
List of Figures VII
1. Introduction 1
2. Model Framework and Pricing Method 9
2.1 Markov-modulated Poisson process 9
2.2 Gold futures price modeling 11
2.3 Least-squares Monte Carlo approach 12
3. Valuation of American Gold Futures Options in a Markov Regime-Switching Jump-Diffusion Economy 15
3.1 Merton measure for the Markov regime-switching jump-diffusion process 16
3.2 Esscher transform for the Markov regime-switching jump-diffusion process 18
3.3 Valuing American gold futures options 22
4. Empirical Analyses and Numerical Illustrations 24
4.1 Empirical results 24
4.2 Pricing performance 34
5. Conclusions and Future Extensions 37
References 39
Appendix A: Distributional properties of RSJM under 44
Appendix B: Solving the Esscher parameters 47
Appendix C: Distributional properties of RSJM under 49
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