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研究生:莊晉國
研究生(外文):Jing-Guo Chuang
論文名稱:NormalInverseGaussianGARCH模型與選擇權定價
論文名稱(外文):Normal Inverse Gaussian GARCH Model and Option Pricing
指導教授:許元春許元春引用關係
指導教授(外文):Yuan-Chung Sheu
學位類別:碩士
校院名稱:國立交通大學
系所名稱:應用數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:英文
論文頁數:18
中文關鍵詞:Normal Inverse Gaussian 分配Esscher 轉換選擇權定價
外文關鍵詞:Normal Inverse GaussianEsscher transformOption Pricing
相關次數:
  • 被引用被引用:0
  • 點閱點閱:264
  • 評分評分:
  • 下載下載:33
  • 收藏至我的研究室書目清單書目收藏:1
這篇論文用NIG GARCH 的模型去描述財務市埸資產的log return。在這樣的模型假設下,我們可以經由Esscher transform的方法來做資產的定價,而這種方法定出來的價格可以用動態效用函數的架構來說明其合理性。
This article uses the NIG GARCH model, the GARCH model with Normal inverse
Gaussian innovation, to model the financial asset return. Under this model, we can
pricing derivatives via Conditional Esscher transform. The pricing result can be justified
by dynamic power utility framework.
1 Introduction 2
2 Generalized hyperbolic distribution 2
2.1 Generalized hyperbolic distribution . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Generalized inverse Gaussian distribution . . . . . . . . . . . . . . . . . . . 3
2.3 Alternative parameterization of NIG . . . . . . . . . . . . . . . . . . . . . . 3
2.4 The GARCH NIG model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Pricing Derivative Under NIG GRACH Model 5
3.1 Conditional Esscher Transform . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Change of measure for the NIG GARCH(1,1) model . . . . . . . . . . . . . 9
4 Estimation 11
5 Numerical Examples 11
6 Conclusion and Further Work 13
7 Appendix 13
7.1 Modified Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.2 Moment structure of Generalized Inverse Gaussian . . . . . . . . . . . . . . 14
7.3 Gradients of the GARCH NIG models. . . . . . . . . . . . . . . . . . . . . . 15
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[11] Gerber, Hans U., and Elias S. W. Shiu. 1994. ”Option Pricing by Esscher Transforms
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