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研究生:陳玉玲
研究生(外文):Yu_Lin Chen
論文名稱:NGARCH模型中選檡權之定價:應用於臺指選擇權
論文名稱(外文):The NGARCH Option Pricing Model: Application to TAIEX Options
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
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:2002
畢業學年度:90
語文別:英文
論文頁數:42
中文關鍵詞:臺灣加權股價指數選擇權蒙地卡羅法臺指選擇權報酬率
外文關鍵詞:NGARCHEmpirical Martingale SimulationTaiwan Stock Exchange Capitalization Weighted Stock IndexTAIEXMonte Carlo SimulationreturnBlack-Scholes Model
相關次數:
  • 被引用被引用:3
  • 點閱點閱:668
  • 評分評分:
  • 下載下載:182
  • 收藏至我的研究室書目清單書目收藏:3
這篇論文假設選擇權標的物之報酬率遵循離散性NGARCH模型,進而採風險中立機率測度定出選擇權價格,並使用修正的蒙地卡羅法 (改稱為Empirical Martingale Simulation) 來計算其數值評價。最後結合這些技巧,應用在2001年12月24日上巿的臺灣加權股價指數選擇權 (Taiwan Stock Exchange Capitalization Weighted Stock Index),研究結果顯示這個估價模型的確優於Black-Scholes 模型。
Following the work of Black and Scholes, we consider a
discrete time option model of the NGARCH asset return process.
At the same time, a new numerical method named by
Empirical Martingale Simulation (EMS) takes the place of crude Monte Carlo Simulation (MCS) to calculate the generated option price. Combining these techniques, we investigate the
Taiwan Stock Exchange Capitalization Weighted Stock Index
(TAIEX) options which were introduced on December 24, 2001.
The result shows that the valuation model is better than the
Black-Scholes model.
1. Introduction
2. Preliminary
2.1 Randon-Nikodym Theorem
2.2 Conditional Expectation
2.3 Conditional Probability
2.4 Conditional Distribution and Probability Density Function
2.5 Conditional Variance
3. Conditional Heteroskedastic Model
3.1 The Generalized AutoRegressive Conditional
Heteroskedastic (GARCH) Model (p,q)
3.2 The Non-linear Asymmetric GARCH (NGACH) Model (p,q)
4. Valuation of Options
4.1 The locally Risk-Netural Probability Measuer
4.2 NGARCH under P
5. Numerical Method: Empirical Martingale Simulation
5.1 Martingale Property in Monte Carlo Simulation
5.2 Strong Law of Large Numbers
5.3 Central Limit Theorem
5.4 Computational Efficiency
6. Taiwan Stock Exchange Capitalization Weighted Stock Index
Options
6.1 The NGARCH(1,1) Applied to TAIEX Options
6.2 Numerical Results
7. Conclusion
1. Billingsley, P. (1995) Probability and Measure,3rd
edition, John Wiley & Sons Inc.
2. Black, F. and M. Scholes (1975) "The pricing of Options
and Corporate Liabilities," Journal of Political Economy
81, 637-659.
3. Bollerslev, Tim (1986) "Generalized Autoregressive
Conditional Heteroskedasticity," Journal of Econometrics 31,
307-327.
4. Breiman, Leo (1992) Probability, SIAM.
5. Duan, J.-C. (1995) "The GARCH Option Pricing
Model," Mahtematical Finance 5, 13-32.
6. Duan, J.-C. (1996) "Cracking the Smile," Risk 9 (December),
55-59.
7. Duan, J.-C. and J.G. Simonato, (1998) "Empirical Martingale
Simulation for Asset Prices," Management Science 44,
1218-1233.
8. Duan, J.-C. (1999) "Conditional Fat-Tailed Distributions
and the Volatility Smile in Options," working paper, Hong
Kong University of Science and Technology.
9. Duan, J.-C., G. Gauthier and J.G. Simonato
(2000) "Asymptotic Distribution of the EMS
Option Price," Management Science 47, 1122-1132.
10. Duan, J.-C. (2000) "Pricing Hang Seng Index Options around
the Asian Financial Crisis - A GARCH Approach,"
Journal of Banking and Finance 25, 1989-2014.
11. Hull, J.C. (2000) Options, Futures, & Other
Derivatives, 4rd edition, Prentice-Hall.
12. Liu, D. (1990) "Option Pricing with Futures-Style
Margining,"Journal of Futures Market 10, 327-338.
13. Pliska, S.R. (1997) Introduction to Mathematical
Finance, Blackwell.
14. Resnick, S.I. (1999) A Probability Path, Birkhauser
Bosten.
15. Tsay, R.S. (2002) Analysis of Financial Time Series, John
Wiley & Sons, Inc..
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