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| 研究生： |
李章益 Li, Chang Yi |
|---|---|
| 論文名稱： |
馬可夫狀態轉換市場下之選擇權定價:雙重 Esscher trnasform 下馬可夫可調控高斯HJM 模型 Valuation Of Options In A Markovian Regime-Switching Market : Markov-Modulated Gaussian HJM Model by Double Esscher Transform |
| 指導教授： |
陳松男
Chen, Son Nan 江彌修 Chiang, Mi Hsiu |
| 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： | 2013 |
| 畢業學年度： | 102 |
| 語文別： | 英文 |
| 論文頁數： | 80 |
| 中文關鍵詞： | 歐式選擇權 、馬柯夫鏈 、卜松過程 、波動叢聚 |
| 外文關鍵詞： | European-style options |
| 相關次數： | 點閱：183 下載：10 |
| 分享至: |
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有越來越多的學術研究顯示，在著名的 Black-Scholes 金融市場下幾何布朗運動並不能描述一些標的資產價數據中，比如標的資產的報酬的分布有厚尾、偏斜、及波動叢聚的現象，而馬可夫可調控狀態轉換的金融保險模型似乎比相對於經典的金融保險模型而言，更能貼近現實中的金融數據。在風險的觀點中，馬可夫可調控的模型有這樣一個優點: 此模型可以隨外界環境 (經濟體的好壞、政府的政策等) 改變自身模型的風險，使得證劵公司進而可以調整自身的政策。
另外一方面，在傳統上 Esscher transform 的測度轉換架構下，無法有足夠的自由度(解集合)使得在馬可夫可調控的狀態轉換過程下之資產動態達到平睹過程的條件，因此本篇論文也致力於發展雙重 Esscher transform 的轉換技巧，使得標的資產可以使用兩種不同的馬可夫鍊容納吸收來自經濟體雙重影響。
The celebrated Black-Scholes financial market is based on a geometric Brownian motion to capture the price dynamics of underlying assets. However, a lot of academic studies reveal that this assumption for assets price dynamics cannot provide realistic description for some important empirical behavior of financial returns such as a kurtosis, a skewness, and volatilities clustering the return’s distribution. Compared with the classical risk model or finance model, the Markov-modulated model or Markovian regime-switching model can provide a better fit to the reality data of insurance and finance. In risk or financial theory, regime-switching risk under Markov-modulated process can capture the feature such that changed environment, such as economic growth or recession, government political, which helps the insurance policies of insurance companies to change their policies.
On the other hand, classical Esscher transform cannot provide sufficient degree of freedom, which is solution of set, such that the underlying assets under Markov-modulated regime-switching process are a martingale process. Hence, this paper is also devoted to considering the mythology of double Esscher transform which accommodate two different Markov chain capturing different effects on economics.
Contents
Abstract ii
Chapter 1 Introduction 1
Chapter 2 Valuation Of Quanto Options In A Markovian Regime-Switching Market: A Markov-Modulated Gaussian HJM Model 5
2.1 Introduction 5
2.2 Regime-switching model 7
2.3 Risk-neutral Martingale measure via Esscher transform 10
2.4 Valuation of European quanto options 13
2.5 Conclusions 19
Chapter 3 Valuation Of Currency Options Under A Regime-Switching Gaussian HJM Model 20
3.1 Introduction 20
3.2 Econometric analysis of spot-FX rate markets 23
3.3 Econometric analysis of yields and bond market via RSBM 35
3.4 European currency options 42
3.5 Empirical study and numerical illustration 51
3.6 Conclusions 57
Chapter 4 Conclusions 59
Appendix A of Chapter 2 60
Change of parameters under new measure 60
Appendix B of Chapter 2 63
Lemma B 63
Case1: Options struck in a foreign currency 63
Case 2: A foreign equity call stuck in domestic currency 64
Case3: A guaranteed-exchange rate foreign equity call option 65
Case 4: An equity-linked foreign exchange call 67
Appendix A of Chapter 3 70
Appendix B of Chapter 3 74
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