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研究生:黃繼宗
研究生(外文):Huang, Chi-Tsung
論文名稱:離散型亞式選擇權定價:分析解及數值解
論文名稱(外文):Pricing Discrete Asian Options: Analytical and Numerical Solutions
指導教授:棗厥庸棗厥庸引用關係
指導教授(外文):Tsao, Chueh-Yung
學位類別:碩士
校院名稱:長庚大學
系所名稱:企業管理研究所
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:48
中文關鍵詞:離散型亞式選擇權控制變數法封閉解泰勒展開式
外文關鍵詞:Discrete Asian OptionControl Variate TechniqueClosed-Form SolutionTaylor Expansion
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  • 被引用被引用:0
  • 點閱點閱:188
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  • 下載下載:49
  • 收藏至我的研究室書目清單書目收藏:0
檢視過去的文獻中,大部分的學者多將研究焦點放在連續型的亞式選擇權訂價,然而在市場上的相關商品,大多使用離散型的平均價格做為計算的標準,使得訂價的準確度降低許多,由此,本文提出有效率的解決方式對歐式及美式的離散平均亞式選擇權進行訂價。本文以Bouaziz, Briys, and Crouhy (1994) 和 Taso, Chang, and Lin (2003)所提出的方法為基礎,利用泰勒展開式對離散型平均價格亞式選擇權進行訂價,進而得出準確的分析解。除了推導出訂價分析解,本文亦針對所得分析解推導避險參數,並進行敏感度分析。接下來,本文再使用所得出的歐式亞式選擇權分析解,利用控制變數法提升美式亞式選擇權的訂價效率。
While in the literature most studies on pricing focus on continuous Asian options, in this thesis we provide efficient solutions for both European and American discrete average price Asian options. The method used for deriving the approximation formula for European Asian options is based on the idea of Bouaziz, Briys, and Crouhy (1994) and Taso, Chang, and Lin (2003) in which the Taylor expansion is used to obtain the approximation formulae for continuous average strike Asian options. By using the Taylor expansion to the second order, a simple and accurate solution can be obtained. Beside the approximation formulae, this thesis also discusses the hedge ratio about the pricing formulae. Furthermore, the approximation formula for the European Asian option can further be used to enhance the efficiency of the pricing of the American Asian options when using the numerical method.
指導教授推薦書 i
口試委員審定書 ii
授權書 iii
誌謝 v
中文摘要 vi
Abstract vii
Chapter 1. Introduction 1
1.1 Background 2
1.2 Motivations and Objectives 3
1.3 Structures of the Thesis 5
Chapter 2. Literature Review 6
2.1 Continuous Asian Options 6
2.2 Discrete Asian Options 8
Chapter 3. The European Asian Options Model 10
3.1 Pricing of Discrete Asian Options 10
3.2 Pricing of Continuous Asian Options 14
3.3 Hedge Ratios 15
Chapter 4. Numerical Analysis 17
4.1 Numerical Results of the European Asian Options 17
4.2 Numerical Results of Hedge Ratios 20
Chapter 5. Pricing of Discrete American Asian Options 23
5.1 The Model of American Asian Options 23
5.2 Numerical Results of the American Asian Options 25
Chapter 6. Conclusions 29
References 31
Appendix 43
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16.Longstaff, F.A., Schwartz, E.S. (2001), Valuing American options by simulations: A simple least-squares approach. The Review of Financial Studies, 14, 113–147.
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19.Nielsen, J. A., Sandmann, K.: Pricing bounds on Asian options. Journal of Financial and Quantitative Analysis, 38, 2 (2003), 449–473.
20.Raymar, S. B., Zwecher, M. J. (1997), A Monte Carlo valuation of American call options on the maximum of several stocks. Journal of Derivatives, 5, 1 (1997), 7–23.
21.Tsao, C.-Y., Chang, C.-C., Lin, C.-G.: Analytic approximation formulae for pricing forward-starting Asian options. Journal of Futures Markets, 23, 5 (2003), May, 487–516.
22.Turnbull, S., Wakeman, L.: A quick algorithm for pricing European average options. Journal of Financial and Quantitative Analysis, 26 (1991), 377–389.
23.Vorst, T.C.F.: Prices and hedge ratios of average exchange rate options. Journal of Financial and Quantitative Analysis, 26 (1992), 337-389.
24.Zhang, J.E.: A semi-analytic method for pricing and hedging continuously sampled arithmetic average rate options. Journal of Computational Finance, 5 (2001), 59–79.
25.Zhang, J.E.: Pricing Continuously Sampled Asian Options with Perturbation Method. Journal of Futures Markets, 23, 6 (2003), 535-560.
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