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研究生:張明淇
論文名稱:有跳躍的GARCH模型
論文名稱(外文):GARCH Models With Jumps
指導教授:許元春許元春引用關係
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:2005
畢業學年度:93
語文別:中文
論文頁數:34
中文關鍵詞:跳躍
外文關鍵詞:GARCHJump
相關次數:
  • 被引用被引用:0
  • 點閱點閱:519
  • 評分評分:
  • 下載下載:38
  • 收藏至我的研究室書目清單書目收藏:1
在這一篇文章裡,我們主要是用一個含有跳躍項的GARCH模型來描述匯率市場的行為,並且比較有跳躍項及沒有跳躍項兩者之間的差異。此外,我們還利用平賭理論以及效用最佳化的論點來推導出在風險中立下所對應的隨機過程並且進而利用蒙地卡羅模擬來計算在我們模型之下的選擇權價格。
In this paper, we mainly use the GARCH model with Jumps to describe the
exchange rates market and compare the performance of models with
jumps and without jumps. In addition, we will use the martingale
theory and the argument of the utility maximization to derive the
risk-neutral process and use the Monte Carlo simulation to find
the option price.
1 Introduction(1)
2 Model(2)
2.1 Setup(2)
2.2 Statistics Description(4)
3 Option Pricing in Risk-Neutral(5)
4 Empirical Research(9)
4.1 Estimation About Parameters(10)
4.2 Data Description(10)
4.3 Empirical Analysis(11)
5 Conclusion(13)
Reference(15)
Appendices(17)
Alireza Javaheri, Paul Wilmott and Espen G. Hau(2002) "GARCH And Volatility Swaps"
Claudla Kluppelberg, Alexander Lindner and Ross Maller(2004)
"A Continuous-Time GARCH Process Driven By A Levy Process:
Stationarity And Second-Order Behaviour" J. Appl. Prob. 41,
601-622(2004)}
Francis A. Longstaff and Eduardo S. Schwartz(2001) "Valuing
American Options by Simulation: A Simple Least-Squares Approach" The Review of Financial Studies Spring 2001 Vol. 14, No. 1, pp.113-147
Giovanni Barone-Adesi, Robert Engle, and Loriano Mancini(2004) "GARCH Options in Incomplete Markets"
Jan Kallsen "Derivative Pricing Based on Local Utility
Maximization"
J.Duan(1995) "The GARCH Option Pricing Model" Mathematical
Finance, Vol. 5, No. 1(January 1995),13-32
J. Duan and Jason Z. Wei(1999) "Pricing Foreign Currency and
Cross-Currency Options Under GARCH"
J. Duan, P. Ritchken, Z. Sun(2004) "Jump Starting GARCH: Pricing and Hedging Options with Jumps in Returns and Volatilities"
J. Duan, P. Ritchken, Z. Sun(2004) "Approximating GARCH-Jump
Models, Jump-Diffusion Processes, and Option Pricing"
J. Duan, Genevi\`{e}ve Ganthier, Caroline Sasseville, Jean-Guy Simonato(2004) "Approximating the GJR-GARCH and EGARCH Option Pricing Models Analytically"
Joshua V. Rosenberg and Robert F. Engle(2001) "Empirical Pricing Kernels"
Marco Frittelli(2000) "The Minimal Entropy Martingale Measure And The Valuation Problem In Incomplete Markets" Mathematical Finance, Vol. 10, No. 1(January 2000) 39-52
Ole E. Barndorff-Nielson, Elisa Nicolato and Neil Shephard(2001) "Some recent developments in stochastic volatility modelling"
Robert Engle(2002) "New Frontiers For ARCH Models" J. Appl.
Econ. 17:425-446(2002)
O.E. Barndorff-Nielsen and N. Shephard(2001) "Integrated OU
Process"
Ruey S. Tsay "Analysis of Financial Time Series" p.79~p.125
Steven L. Heston and Saikat Nandi(2000) "A Closed-Form GARCH
Option Valuation Model" The Review of Financial Studies,
Vol. 13 ,No. 3(Autumn, 2000),585-625
Torben G. Andersen, Tim Bollerslev, Francis X. Diebold and Paul Labys(1999) "The Distribution of Exchange Rate Volatility"
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