| dc.contributor.advisor | 劉明郎 | zh_TW |
| dc.contributor.advisor | Liu, Ming-long | en_US |
| dc.contributor.author (Authors) | 劉桂芳 | zh_TW |
| dc.contributor.author (Authors) | Liu, Kuei-fang | en_US |
| dc.creator (作者) | 劉桂芳 | zh_TW |
| dc.creator (作者) | Liu, Kuei-fang | en_US |
| dc.date (日期) | 2004 | en_US |
| dc.date.accessioned | 17-Sep-2009 13:50:05 (UTC+8) | - |
| dc.date.available | 17-Sep-2009 13:50:05 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Sep-2009 13:50:05 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0917510071 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32605 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 91751007 | zh_TW |
| dc.description (描述) | 93 | zh_TW |
| dc.description.abstract (摘要) | 本論文研究如何由觀測的選擇權市場價格還原風險中立機率測度（等價平賭測度）。首先建構選擇權投資組合的套利模型，其中假設選擇權為單期，到期日時的狀態為離散點且個數有限，並且對應同一標的資產且不同履約價格。若市場不存在套利機會時，可使用拉格朗日乘數法則將選擇權套利模型導出拉格朗日乘子的可行性問題。將可行性問題作為限制式重新建構線性規劃模型以還原風險中立機率測度，並且利用此風險中立機率測度評價選擇權的公正價格。最後，我們以台指選擇權（TXO）為例，驗證此模型的評價能力。 | zh_TW |
| dc.description.abstract (摘要) | This thesis investigates how to recover the risk-neutral probability (equivalent martingale measure) from observed market prices of options. It starts with building an arbitrage model of options portfolio in which the options are assumed to be in one-period time, finite discrete-states, and corresponding to the same underlying asset with different strike prices. If there is no arbitrage opportunity in the market, we can use Lagrangian multiplier method to obtain a Lagrangian multiplier feasibility problem from the arbitrage model. We employ the feasibility problem as the constraints to construct a linear programming model to recover the risk-neutral probability, and utilize this risk-neutral probability to evaluate the fair price of options. Finally, we take TXO as an example to verify the pricing ability of this model. | en_US |
| dc.description.tableofcontents | 摘要..................................................vABSTRACT.............................................vi目次................................................vii圖目次.............................................viii表目次...............................................ix第一章 緒論...........................................1 1.1 研究動機與研究方法............................1 1.2 文章架構......................................2第二章 文獻回顧.......................................3 2.1 PDE與EMM評價模型.............................3 2.2 二元樹與隱含二元樹............................6 2.3 隨機規劃法還原風險中立機率測度................9 2.4 回顧還原風險中立機率測度的方法...............12第三章 由市場價格建構選擇權評價模型..................15 3.1 選擇權的套利模型.............................15 3.2 還原風險中立機率測度.........................20第四章 實證研究......................................28 4.1 資料來源.....................................28 4.2 結果分析.....................................294.2.1評價價格與市場價格之比較........................294.2.2風險中立機率測度的型態..........................40第五章 結論與建議....................................43參考文獻.............................................45附表.................................................47 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0917510071 | en_US |
| dc.subject (關鍵詞) | 評價選擇權 | zh_TW |
| dc.subject (關鍵詞) | 風險中立機率測度 | zh_TW |
| dc.subject (關鍵詞) | 等價平賭測度 | zh_TW |
| dc.subject (關鍵詞) | 線性規劃 | zh_TW |
| dc.subject (關鍵詞) | options pricing | en_US |
| dc.subject (關鍵詞) | risk-neutral probability measure | en_US |
| dc.subject (關鍵詞) | equivalent martingale measure | en_US |
| dc.subject (關鍵詞) | linear programming | en_US |
| dc.title (題名) | 由選擇權市場價格建構具一致性之評價模型 | zh_TW |
| dc.title (題名) | Building a Consistent Pricing Model from Observed Option Prices via Linear Programming | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | Black, F. and M. Scholes (1973), “Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81(3), 637-659. | zh_TW |
| dc.relation.reference (參考文獻) | Churchill, R. V. (1963), “Fourier Series and Boundary Value Problems.” 2nd ed. New York, McGraw-Hill. | zh_TW |
| dc.relation.reference (參考文獻) | Cox, J. and S. Ross (1976), “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics 3, 145-166. | zh_TW |
| dc.relation.reference (參考文獻) | Cox, J., S. Ross, and M. Rubinstein (1979), “Option Pricing: A Simplified Approach.” Journal of Financial Economics 7(3), 229-263. | zh_TW |
| dc.relation.reference (參考文獻) | Derman, E. and I. Kani (1998), “Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility.” International Journal of Theoretical and Applied Finance 1, 7-22. | zh_TW |
| dc.relation.reference (參考文獻) | Harrison, J. and S. Pliska (1981), “Martingales and Stochastic Integrals in the Theory of Continuous Time Trading.” Stochastic Processes and their Applications 11, 215-260. | zh_TW |
| dc.relation.reference (參考文獻) | Haugh, M. (2004), “Martingale Pricing Theory.” Lecture Note, Department of Industrial Engineering and Operation Research, Columbia University. | zh_TW |
| dc.relation.reference (參考文獻) | Ito K. (1951), “On Stochastic Differential Equation Memories.” American Mathematical Society 4, 1-51. | zh_TW |
| dc.relation.reference (參考文獻) | Jackwerth, J. (1997), “Generalized Binomial Trees.” Journal of Derivatives 5(2), 7-17. | zh_TW |
| dc.relation.reference (參考文獻) | Jackwerth, J. (1999), “Option-Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review.” Journal of Derivatives 7(2), 66-82. | zh_TW |
| dc.relation.reference (參考文獻) | King, A. (2002), “Duality and Martingale: A Stochastic Programming Perspective on Contingent Claims.” Mathematical Programming Ser. B 91, 543-562. | zh_TW |
| dc.relation.reference (參考文獻) | Melick, W. and C. Thomas (1997), “Recovering an Asset’s Implied PDF from Option Prices: An Application to Crude Oil During the Gulf Crisis.” Journal of Financial and Quantitative Analysis 32, 91-115. | zh_TW |
| dc.relation.reference (參考文獻) | Rubinstein M. and J. Jackwerth (1997), “Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns.” in: The Legacy of Fisher Black, editor: Bruce N. Lehmann, Oxford University Press, Oxford. | zh_TW |
| dc.relation.reference (參考文獻) | Rubinstein, M. (1994), “Implied Binomial Trees.” Journal of Derivatives 49(3), 771-818. | zh_TW |
| dc.relation.reference (參考文獻) | Sharpe, W. F. (1978), “Investments.” Prentice-Hall International. | zh_TW |
| dc.relation.reference (參考文獻) | Sherrick, B., P. Garcia, and V. Tirupattur (1995), “Recovering Probabilistic Information from Option Markets: Tests of Distributional Assumptions.” Working paper, University of Illinois at Urbana-Champaign. | zh_TW |
| dc.relation.reference (參考文獻) | 楊靜宜 (2004)，選擇權交易策略的整數線性規劃模型，政治大學應用數學研究所碩士論文。 | zh_TW |
