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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 呂育道(Yuh-Dauh Lyuu) | |
dc.contributor.author | Yi-Chia Huang | en |
dc.contributor.author | 黃怡嘉 | zh_TW |
dc.date.accessioned | 2021-06-15T05:26:41Z | - |
dc.date.available | 2013-07-20 | |
dc.date.copyright | 2010-07-20 | |
dc.date.issued | 2010 | |
dc.date.submitted | 2010-07-15 | |
dc.identifier.citation | [1] Black, F., and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 637–659.
[2] Boyle, P. (1986) Options Valuation Using a Three Jump Process, International Options Journal, 3, 7–12. [3] Chesney, M., Jeanblanc, M., and Yor, M. (1997) Brownian Excursion and Parisian Barrier Options, Advances in Applied Probability, 29, 165–184. [4] Costabile, M. (2002) A Combinatorial Approach for Pricing Parisian Options, Decisions in Economics and Finance, 25(2), 111–125. [5] Cox, J.C., Ross, S.A., and Rubinstein, M. (1979) Option Pricing: A Simplified Approach, Journal of Financial Economics, 7, 229–263. [6] Dai, T.-S., and Lyuu, Y.-D. (2005) Pricing Double Barrier Options by Combinatorial Approaches, Advances in Soft Computing-Soft Computing as Transdisciplinary Science and Technology, Muroran, Japan, 1131–1140. [7] Dai, T.-S., and Lyuu, Y.-D. (2010) The Bino-Trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing, Journal of Derivatives, 17, 7–24. [8] Figlewski, S., and Gao, B. (1999) The Adaptive Mesh Model : A New Approach to Efficient Option Pricing, Journal of Financial Economics, 53, 313–351. [9] Hull, J.C. (2006) Options, Futures, and Other Derivatives, 6th edition, Upper Saddle River, NJ: Prentice-Hall. [10] Lyuu, Y.-D. (1998) Very Fast Algorithms for Barrier Option Pricing and the Ballot Problem, The Journal of Derivatives, 5(3), 68–79. [11] Lyuu, Y.-D. (2002) Financial Engineering & Computation: Principles, Mathematics, Algorithms, Cambridge, UK: Cambridge University Press. [12] Lyuu, Y.-D., and Wu, C.-W. (2010) An Improved Combinatorial Approach for Pricing Parisian Options, Decisions in Economics and Finance, 33, 49–61. [13] Pun, C.M. (2007) Trinomial-Tree-Based Combinatorial Methods for the Barrier and Parisian Options, Graduate Institute of Finance, Master Thesis, National Taiwan University of Science and Technology, Taipei, Taiwan. [14] Ritchken, P. (1995) On Pricing Barrier Options, Journal of Derivatives, 3, 19–28. [15] Wu, C.-W. (2008) Pricing Parisian Options: Combinatorics, Simulations, and Parallel Processing, Master Thesis, Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan. [16] 謝劍平 (2003) 期貨與選擇權:財務工程的入門捷徑,台北市:智勝文化。 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46740 | - |
dc.description.abstract | 巴黎選擇權是一種路徑相關的選擇權。Chesney(1997)利用拉普拉斯轉換求解巴黎選擇權的微分方程式,除了這個方法之外,我們也可以利用樹模型評價巴黎選擇權,Lyuu及Wu在2009年提出改進Costabile(2002)的二元樹模型演算法,這個方法在複雜度上有不錯的表現,時間複雜度是O(n2)、而空間複雜度是O(n2)。但使用二元樹評價巴黎選擇權時,會因為障礙價格不一定在格點上而產生收斂跳動之非線性誤差。我們在這篇論文中討論以三元樹模型及bino-trinomial tree這兩種樹模型評價巴黎選擇權並且分析他們各自的複雜度,發現確實可以減少收斂跳動之非線性誤差。
在三元樹模型中,雖然可以解決因為選擇權的障礙價格不一定會落在節點上所造成的非線性誤差,但在組合學的方法中時間複雜度會大幅上升到O(n3)。因此我們再導入bino-trinomial tree這種模型來解決障礙價格所產生的誤差,而時間複雜度也可以維持在O(n2),空間複雜度在O(n),與Lyuu-Wu (2009) 的二元樹模型一樣,所以我們的結果結合了以上所有方法的優點,而且避開其缺點。 | zh_TW |
dc.description.abstract | Parisian option is a path-dependent option. Chesney (1997) uses Laplace transform to derive the PDE for Parisian options. Lattice methods have also been used to price Parisian options. For example, Lyuu and Wu (2008) improve Costabile’s (2002) algorithm, which uses binomial tree model. The time complexity decrease to O(n2), and space complexity is O(n). But when we us binomial option pricing model for pricing Parisian options, there are nonlinearity errors when the barrier is not laid on one of the prices on the tree. In this thesis, we use combinatorial methods in trinomial tree model and bino-trinomial tree model for pricing Parisian options, and these two models do decrease nonlinearity errors.
First we use trinomial tree model. Although there are no nonlinearity errors, the time complexity will rise to O(n3). Then we use the bino-trinomial tree model, which results in a time complexity of O(n2) and a space complexity of O(n), the same as Lyuu and Wu (2008). In conclusion, our method inherits all the strengths of the above methods while avoiding their weaknesses. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T05:26:41Z (GMT). No. of bitstreams: 1 ntu-99-R97922081-1.pdf: 1673604 bytes, checksum: b5740a42bd3ea081b9eea00005dd26e8 (MD5) Previous issue date: 2010 | en |
dc.description.tableofcontents | 口試委員會審定書 i
謝誌 ii 中文摘要 iii Abstract iv 圖目錄 vii 表目錄 viii 第一章 簡介 1 1.1 選擇權 1 1.2 障礙選擇權 2 1.3 巴黎選擇權 3 第二章 模型基本設定 4 2.1 Geometric Brownian motion 4 2.2 Black-Scholes模型 4 2.3 二元樹選擇權評價模型(binomial option pricing model) 5 2.4 三元樹模型(trinomial tree model) 10 2.5 Bino-trinomial tree模型 13 第三章 組合學方法評價巴黎選擇權 15 3.1 二元樹 15 3.1.1 Costabile的演算法 15 3.1.2 Lyuu-Wu的演算法 20 3.2 三元樹 22 3.3 Bino-trinomial tree 25 第四章 數值實驗 30 4.1 撰寫程式所使用的技巧 30 4.1.1 處理大數問題 30 4.1.2 計算組合數的方法 30 4.2 基本參數數據 31 4.3 數值結果 31 第五章 結論 38 參考文獻 39 附錄一 三元樹模型的演算法 41 附錄二 Bino-trinomial tree 模型的演算法 44 | |
dc.language.iso | zh-TW | |
dc.title | 組合學方法評價巴黎選擇權 | zh_TW |
dc.title | Combinatorial Methods for Parisian Options | en |
dc.type | Thesis | |
dc.date.schoolyear | 98-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 金國興(Guo-Xing Jin),戴天時(Tian-Shyr Dai) | |
dc.subject.keyword | 巴黎選擇權,障礙選擇權,選擇權評價,二元樹模型,三元樹模型,三元樹模型,組合方法, | zh_TW |
dc.subject.keyword | Parisian options,barrier options,option pricing,binomial tree,trinomial tree,bino-trinomial tree,combinatorial method, | en |
dc.relation.page | 47 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2010-07-16 | |
dc.contributor.author-college | 電機資訊學院 | zh_TW |
dc.contributor.author-dept | 資訊工程學研究所 | zh_TW |
顯示於系所單位: | 資訊工程學系 |
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