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| 研究生： |
王昭文 |
|---|---|
| 論文名稱： |
隨機利率下選擇權訂價模型 |
| 指導教授： | 廖四郎 |
| 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： | 2002 |
| 畢業學年度： | 90 |
| 語文別： | 英文 |
| 論文頁數： | 80 |
| 相關次數： | 點閱：238 下載：24 |
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Under Gaussian HJM framework, the first goal of the research is to derive the closed-form solution of market-traded contingent claims, such as Taiwanese capped options and under Gaussian HJM framework. I provide the closed-form solutions of generalized capped options (one of the special cases is Taiwanese capped options). However, some contingent claims do not have closed-form solutions, such as long-dated American stock options. Thus, how to develop numerical techniques such as lattice method and Monte Carlo simulation under Gaussian HJM framework is also important for option pricing. The second goal of the research is to provide the numerical methods such as lattice method, and Monte Carlo simulation under Gaussian HJM framework. Unlike the other numerical methods under stochastic interests, our methods can be used to compute the prices of equity derivatives which are related to interest rate, for example, long-dated American stock options.
誌謝
Abstract
Contents-----i
Table and Figures-----iii
Chapter 1. Introduction-----1
1.1 Motivation and Purpose-----1
1.2 Outline of the Research-----4
Chapter 2. Literature Review-----7
2.1 Capped Option-----7
2.2 Implied Spot-price Tree Method-----9
2.3 Monte Carlo Simulation-----10
Chapter 3. Gaussian HJM Framework-----12
Chapter 4. Generalized Capped Options-----16
4.1 Generalized Capped Exchange Options-----16
4.2 Special Cases of Generalized Capped Exchange Options-----19
4.2.1 Taiwanese Capped Options-----19
4.2.1.1 Closed-form solution of Taiwanese Capped Options-----19
4.2.1.2 Properties of Taiwanese Capped Options-----22
4.2.1.3 Delta Jump-----22
4.2.2 Taiwanese Floored Options-----24
4.2.2.1 Closed-form solution of Taiwanese Floored Options-----25
4.2.3 Taiwanese Capped or Floored Options with Exponential Barrier-----27
4.2.4 Other Extensions-----27
4.3 Conclusion for this Chapter-----28
Chapter 5. Implied Spot-price Tree Method-----30
5.1 Forward-Price Methodology and Implied Spot-Price Trees-----30
5.2 Pricing Options under Gaussian HJM Framework-----38
5.2.1 Determination of Parameters for Binomial Tree-----39
5.2.2 Numerical Example-----42
5.2.3 Continuous Time-Varying Dividend Yield Case-----43
5.2.4 Determination of Parameters for Trinomial Tree-----44
5.3 Numerical Results-----47
5.4 Conclusion for this Chapter-----49
Chapter 6. Monte Carlo under Gaussian HJM Framework-----54
6.1 Monte Carlo Method under Gaussian HJM Model-----54
6.1.1 Monte Carlo with Equal Time Interval (Method 1 )-----54
6.1.2 Monte Carlo with Identical Volatility (Method 2)-----57
6.1.3 Case of Continuous Dividend Yield-----60
6.1.4 Variance Reduction Methods-----61
6.2 Pricing Method for High-Dimensional Contingent Claims-----63
6.3 Numerical Results-----66
6.4 Conclusion for this Chapter-----66
Chapter 7. Conclusions-----67
References
Table and Figures
Table 2-1 Capped Options in Taiwan Stock Exchange-----8
Table 4-1 Prices of Plain Vanilla Call Option and Taiwanese Capped Option-----23
Table 4-2 Prices of Plain Vanilla Put Option and Taiwanese Floored Option-----26
Table 5-1 Prices of European Put Option from Implied Spot-Price Trees with Different Time Steps-----51
Table 5-2 Prices of American Call Options with Zero Dividend Payout from Implied Spot-Price Trees with Different Time Steps-----52
Table 5-3 Prices of American Put Options from Implied Spot-Price Trees with Different Time Steps-----53
Table 6-1 European put option with different number of simulations and time to maturity-----64
Table 6-2 European Call Option on Coupon-bearing Bond with Different Number of Simulations and Time to Maturity-----65
Figure 1-1 Procedure of the Research-----6
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