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 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 viAbstract viiChapter 1. Introduction 11.1 Background 21.2 Motivations and Objectives 31.3 Structures of the Thesis 5Chapter 2. Literature Review 62.1 Continuous Asian Options 62.2 Discrete Asian Options 8Chapter 3. The European Asian Options Model 103.1 Pricing of Discrete Asian Options 103.2 Pricing of Continuous Asian Options 143.3 Hedge Ratios 15Chapter 4. Numerical Analysis 174.1 Numerical Results of the European Asian Options 174.2 Numerical Results of Hedge Ratios 20Chapter 5. Pricing of Discrete American Asian Options 235.1 The Model of American Asian Options 235.2 Numerical Results of the American Asian Options 25Chapter 6. Conclusions 29References 31Appendix 43
 1.Benhamou, E., Duguet, A.: Small dimension PDE for discrete Asian options. Journal of Economic Dynamics & Control, 27 (2003), 2095–2114.2.Black, F., Scholes, M.: The pricing of options and corporate liabilities. Journal of Political Economy, 81 (1973), 637–659.3.Bouaziz, L., Briys, E., Crouhy, M.: The pricing of forward-starting Asian options. Journal of Banking and Finance, 18 (1994), 823–839.4.Chang, C.-C., Tsao C.-Y.: Efficient and accurate quadratic approximation methods for pricing Asian options. (2004) Paper presented at the Asian FA/TFA/FMA 2004 Conference, Taipei, Taiwan, July 12-14, 2004.5.Cox, J. C., Ross S. A., Rubinstein M.: Option Pricing: A Simplified Approach. Journal of Financial Economics, 7 (1979), 229–263.6.Curran, M.: Valuing Asian and portfolio options by conditioning on the geometric mean price. Management Science, 40, 12 (1994), 1705–1711.7.Duan, J.-C., Simonato, J.-G.: Empirical martingale simulation for asset prices. Management Science, 44, 9 (1998), 1218–1233.8.Gastineau, G.: A better control variate for pricing standard Asian options. Journal of Financial Engineering, 2 (1993), 207–216.9.Geman, H., Yor, M.: Bessel processes, Asian options and perpetuities. Mathematical Finance, 3 (1993), 349–375.10.Grant D., Vora, G., Weeks, D.: Simulation and the early-exercise option problem. Journal of Financial Engineering, 5, 3 (1996), 211–227.11.Hull, J., White, A.: The use of the control variate technique in option pricing. Journal of Financial and Quantitative Analysis, 23 (1988), 237–25112.Hull, J., White, A.: Valuing derivative securities using the explicit finite difference method. Journal of Financial and Quantitative Analysis, 24 (1990), 87–100.13.Hull, J., White, A.: Efficient procedures for valuing European and American path-dependent options. Journal of Derivatives, 1 (1993), 21–31.14.Ju, N.: Pricing Asian and basket options via Taylor expansion. Journal of Computational Finance, 5 (2002), 79–103.15.Levy, E.: Pricing European average rate currency options. Journal of Banking and Finance, 11 (1992), 474–491.16.Longstaff, F.A., Schwartz, E.S. (2001), Valuing American options by simulations: A simple least-squares approach. The Review of Financial Studies, 14, 113–147.17.Kemma, A., Vorst, A.: A pricing method for options based on average asset prices. Journal of Banking and Finance, 2 (1990), 52–66.18.Milevsky, M. A., Posner, S. E: Asian options, the sum of lognormals and the reciprocal gamma distribution. Journal of Financial and Quantitative Analysis, 33 (1998), 409–422.19.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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 1 離散型亞式選擇權評價及避險係數的封閉解

 1 22. 蔡金津，”超臨界流體應用於高分子加工技術”， 化工資訊與商情 ，第五期，p.41，2003。 2 22. 蔡金津，”超臨界流體應用於高分子加工技術”， 化工資訊與商情 ，第五期，p.41，2003。 3 22. 蔡金津，”超臨界流體應用於高分子加工技術”， 化工資訊與商情 ，第五期，p.41，2003。

 1 遠期生效亞式選擇權之分析解－考慮隨機波動效果 2 利用數值方法評價算數平均式亞式選擇權 3 亞式選擇權定價之Black-Scholes方程的解析方法 4 傅利葉轉換於亞式選擇權評價上之應用性研究 5 離散型亞式選擇權評價及避險係數的封閉解 6 雨量選擇權的定價與避險 7 美式選擇權定價之數值方法 8 Black-Scholes方程式的數值模擬與選擇權定價問題之相關應用 9 選擇權定價與行為分析之探討-BlackandScholes模型和隨機波動模型之應用 10 美式選擇權定價之動態規劃方法 11 亞式選擇權之評價與模擬之研究 12 基於選擇權定價、效用函數、風險值預測和概似函數，比較多變量波動率模型 13 關於選擇權定價的三則短論 14 RBF在選擇權定價上之應用 15 評價移動平均交換選擇權—數值方法與解析近似法

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