時變參數下之雙障礙選擇權評價

Chih-I Chen; 陳芝亦

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23657

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	Chih-I Chen	en
dc.contributor.author	陳芝亦	zh_TW
dc.date.accessioned	2021-06-08T05:06:49Z	-
dc.date.copyright	2011-07-07
dc.date.issued	2011
dc.date.submitted	2011-06-29
dc.identifier.citation	[1] Amin, Kaushik I. “On the Computation of Continuous Time Option Pricing Using Discrete Approximations.” Journal of Financial and Quantitative Analysis, 26, No. 4 (December 1991), 477–495. [2] Black, F and J. Cox. Valuing Corporate Securities: Some Effects of Bond Indeture Provisions. Journal of Finance, 31, No. 2, (May 1976), 351–367. [3] Black, Fischer and Myron Scholes. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81, No. 3 (May–June 1973), 637–654. [4] Boyle, Phelimand and Sok Hoon Lau. “Bumping Up against the Barrier with the Binomial Method.” The Journal of Derivatives, 1, No.4 (Summer 1994), 6–14. [5] Costabile, M. “Extending the Cox-Ross-Rubinstein Algorithm for Pricing Options with an Exponential Boundary.” In Proceedings of Algorithm Conference on Scientific Computing, Slovakia, September 2002, 23–32. [6] Cox, John C., Stephen A. Ross, and Mark Rubinstein. “Option Pricing: A Simpliﬁed Approach.” Journal of Financial Economics, 7, No. 3 (September 1979), 229–263. [7] Dai, Tian-Shyr and Yuh-Dauh Lyuu. “The Bino-trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing.” In Proceedings of FMA European Conference, Prague, Czech Republic, June 4–6, 2008. [8] Dai, Tian-Shyr, Yuh-Dauh Lyuu, and Chuan-Ju Wang. “A Novel Tree Model for Evaluating Credit Risk Based on Enhanced Structural Model.” In Proceedings of the 44th Euro Working Group on Financial Modelling Meeting (EWGFM), Costa Rica, May 3–6, 2009. [9] Dai, Tian-Shyr, Chuan-Ju Wang, and Yuh-Dauh Lyuu. “A Novel Tree Model for Evaluating Corporate Debts with Complex Liability Structures and Debt Covenants.” In Proceedings of the Asian Finance Association 2010 Conference, Hong Kong, June 29–July 2, 2010. [10] Dai, Tian-Shyr and Yuh-Dauh Lyuu. “The Bino-Trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing.” Journal of Derivatives, 17, No. 4 (Summer 2010), 7–24. [11] Derman, E., I. Kani, Deniz Ergener, and Indrajit Bardhan. “Enhanced Numerical Methods for Options with Barriers.” Financial Analysts Journal, 51, No. 6 (November–December 1995), 65–74. [12] Derman, E., I. Kani, and N. Chriss. “Implied Trinomial Trees of the Volatility Smile.” The Journal of Derivatives, 3, No. 4 (Summer 1996), 7–22. [13] Dupire, Bruno. “Pricing with a Smile.” Risk, 7, No. 1 (January 1994), 18–20. [14] Figlewski, Stephen and Bin Gao. “The Adaptive Mesh Model: A New Approach to Efficient Option Pricing.” Journal of Financial Economics, Vol. 53 (1999), 313–351. [15] Heston, Steven L. “A Closed-Form Solution for Options with Stochastic Volatilities with Applications to Bond and Currency Options.” The Review of Financial Studies, 6, No. 2 (1993), 327–343. [16] Hull, John C. and Alan White. “The Pricing of Options on Assets with Stochastic Volatilities.” The Journal of Finance, 42, No. 2 (June 1987), 281–300. [17] Hull, John C. Options, Futures & Other Derivatives. 5th ed. Englewood Cliffs, NJ: Prentice Hall, 2003. [18] Li, Yanmin. “A New Algorithm for Constructing Implied Binomial Trees: Does the Implied Model Fit Any Volatility Smile?” Journal of Financial Engineering, Vol. 4 (2000), 69–95. [19] Lyuu, Yuh-Dauh. “Very Fast Algorithms for Barrier Option Pricing and the Ballot Problem” The Journal of Derivatives, 5, No. 3 (Spring 1998), 68–79. [20] Lyuu, Yuh-Dauh. Financial Engineering and Computation. Cambridge, UK: Cambridge University Press, 2002. [21] Merton, R.C. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4, No. 1 (Spring 1973), 141–183. [22] Ritchken, Peter. “On Pricing Barrier Options.” The Journal of Derivatives, 3, No. 2 (Winter 1995), 19–28.
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23657	-
dc.description.abstract	障礙選擇權是一種路徑相依的衍生性金融產品，其價格決定於資產價格是否碰觸到給定的障礙H。一般而言，在許多評價樹模型中，分配誤差與非線性誤差會導致評價結果無法平滑收斂。本論文進一步探討雙障礙與資產年化波動率σ(t)為時變的函數，以符合實際的市場條件。然而這會導致在傳統的評價樹模型中遭遇困難。首先，隨時間變動的雙障礙會造成障礙沒有落在評價樹的節點上，而使非線性誤差更大。而隨時間波動的資產年化波動率σ(t)會使傳統評價樹每一期的分支無法接合，並使計算複雜度呈指數成長。 Amin（1991）提出的二元樹模型可允許標的物資產年化波動率為隨時間變動的函數，並能以O(n2)的計算複雜度評價陽春選擇權。Dai and Lyuu（2008, 2010）所提出的bino-trinomial tree模型可藉由調整評價樹的結構，大幅降低非線性誤差並快速而精確地評價多種金融產品。在本篇論文中，我們延伸應用了Dai and Lyuu（2008, 2010）提出的bino-trinomial tree模型與Amin（1991）的模型，以用來評價時變波動率與雙障礙皆為隨時間變化的指數函數的雙障礙選擇權價格。我們以蒙地卡羅模擬驗證了我們評價模型的正確性：在計算複雜度O(n2)下做出精確的評價。同時，數值結果顯示計算出的時變波動率與非線性障礙邊界下雙障礙選擇權價格能夠快速與平滑地收斂，而不會產生巨幅震盪。	zh_TW
dc.description.provenance	Made available in DSpace on 2021-06-08T05:06:49Z (GMT). No. of bitstreams: 1 ntu-100-R98922127-1.pdf: 709729 bytes, checksum: 57fe82c5af6d0aaf25a55e8b20232c16 (MD5) Previous issue date: 2011	en
dc.description.tableofcontents	口試委員會審定書 i 誌謝 ii 摘要 iii ABSTRACT iv 圖目錄 vi 表目錄 vii 第一章導論 1 1.1 障礙選擇權 1 1.2 論文架構 4 第二章背景知識 6 2.1 二元樹評價模型與估計誤差 6 2.2 BTT評價模型 8 2.3 時變波動率下Black-Scholes Formula的封閉解 10 2.4 時變波動率下的樹狀評價模型 11 第三章時變參數下之障礙選擇權評價模型 16 3.1符號與樹狀評價模型的定義 16 3.2單一障礙選擇權樹狀評價模型之建構 17 3.3 非線性障礙邊界下單一障礙選擇權樹狀評價模型之建構 23 3.4非線性障礙邊界下雙障礙選擇權樹狀評價模型之建構 26 第四章數值結果 32 4.1時變波動率下單一障礙選擇權評價結果 32 4.2時變波動率與非線性障礙邊界下障礙選擇權評價結果 34 4.3時變波動率與非線性障礙邊界下雙障礙選擇權評價結果 35 第五章總結 36 附錄 37 參考文獻 38
dc.language.iso	zh-TW
dc.title	時變參數下之雙障礙選擇權評價	zh_TW
dc.title	Pricing Double-Barrier Options with Time-Varying Parameters	en
dc.type	Thesis
dc.date.schoolyear	99-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	戴天時(Tian-Shyr Dai),金國興(Guo-Xing Jin),張經略(Ching-Lueh Chang)
dc.subject.keyword	障礙選擇權,時變波動率,非線性障礙,樹模型,非線性誤差,	zh_TW
dc.subject.keyword	barrier option,time-varying volatility,non-linear barrier,tree model,nonlinearity error,	en
dc.relation.page	39
dc.rights.note	未授權
dc.date.accepted	2011-06-29
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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