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題名 應用賽局理論評價選擇權
作者 陳韻竹
貢獻者 劉明郎
陳韻竹
關鍵詞 評價選擇權
風險中立機率測度
等價平賭測度
賽局理論
線性規劃
日期 2006
上傳時間 17-Sep-2009 13:48:34 (UTC+8)
摘要 本論文利用市場觀測的選擇權買價與賣價，將市場的交易行為描述為兩人零合賽局，其中參賽者為投資人與市場機制，分別建立雙方的最佳策略模型。假設標的資產到期日的價格為離散點且個數有限，當市場不存在套利機會，也就是投資人最佳策略時報償為零時，可利用賽局線性規劃模型導出隱含於市場價格的風險中立機率測度。此模型不須對標的資產價格的機率分配做任何假設，也不須計算波動度，就可利用資產價格的平賭性質，以還原的風險中立機率測度為選擇權作合理的定價。最後，以台指選擇權(TXO)為例，驗證本模型的評價能力，且再次證實資產價格的風險中立機率分佈與一般常假設的對數常態分佈有落差。
參考文獻 Black, F. and M. Scholes, 1973, The pricing of options and corporate liabilities. Journal of political Economy 81(3), 637-659.
Boyle, P. P. and T. Vorse, 1992, Option replication in discrete time with transaction cost. Journal of Finance 47(1), 271-294.
Cox, J. C., S. Ross, M. Rubinstein 1979, Option pricing: A simplified approach. Journal of Financial Economic 3,145-166.
Harrison, M. and D. Kreps, 1979, Martingale and arbitrage in multiperiod security markets. Journal of Economic Theory 20, 381-408.
Jackwerth, J. C., 2000, Recovering risk aversion from option prices and realized returns. The Review of Financial Studenies 13(2), 433-451.
King, A. 2002, Duality and martingale: A Stochastic programming perspective on contingent claims. Mathematical Programming Ser. B 91, 543-562.
Kline, J., 2000, For the Student: Basic game theory. The Australian Economic Review 33(4), 381-387.
Leland, H., 1985. Option pricing and replication with transaction costs. Journal of finance 40(5), 1283-1301.
Melinkov A. A. and Y. G. Petrachenko, 2005, On option pricing in binomial market with transaction costs. Finance and Stochastics 9, 141-149.
Prasad C. and J. Somesh, 2001, Randomized stopping times and American option pricing with transaction costs. Mathematical Finance 11(1), 33-77.
Rubinstein, M., 1994, Implied Binomial Trees. Journal of Finance 49(3), 771-818.
Rubinstein, M. and J. Jackwerth, 1996, Recovering probability distributions from option prices. The Journal of Finance 51(5), 1611-1631.
Steven R., 2000, “Option exercise games: the intersection of real options and game theory. Journal of Applied Corporate Finance 13(2), 99-107.
Ales C., 2004, Mathematical Techniques in Finance. Tools for Incomplete Markets. Princeton University Press, New Jersey.
Neftci, S.N., 2004, An Introduction to the Mathematics of Financial Derivatives. Academic press, New York.
張瓊芳，2005，由市場的選擇權價格還原風險中立機率分布，國立政治大學應用數學系碩士論文，台北。
劉桂芳，2005，由選擇權市場價格建構具一致性之評價模型，國立政治大學應用數學系碩士論文，台北。
描述 碩士
國立政治大學
應用數學研究所
94751014
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0094751014
資料類型 thesis
dc.contributor.advisor 劉明郎zh_TW
dc.contributor.author (Authors) 陳韻竹zh_TW
dc.creator (作者) 陳韻竹zh_TW
dc.date (日期) 2006en_US
dc.date.accessioned 17-Sep-2009 13:48:34 (UTC+8)-
dc.date.available 17-Sep-2009 13:48:34 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:48:34 (UTC+8)-
dc.identifier (Other Identifiers) G0094751014en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32591-
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) 94751014zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) 本論文利用市場觀測的選擇權買價與賣價，將市場的交易行為描述為兩人零合賽局，其中參賽者為投資人與市場機制，分別建立雙方的最佳策略模型。假設標的資產到期日的價格為離散點且個數有限，當市場不存在套利機會，也就是投資人最佳策略時報償為零時，可利用賽局線性規劃模型導出隱含於市場價格的風險中立機率測度。此模型不須對標的資產價格的機率分配做任何假設，也不須計算波動度，就可利用資產價格的平賭性質，以還原的風險中立機率測度為選擇權作合理的定價。最後，以台指選擇權(TXO)為例，驗證本模型的評價能力，且再次證實資產價格的風險中立機率分佈與一般常假設的對數常態分佈有落差。zh_TW
dc.description.tableofcontents 摘要 iii
ABSTRACT iv
目錄 v
圖目錄 vi
表目錄 vii
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 Black-Scholes歐式選擇權評價模型 3
2.2平賭過程評價方法 5
2.3還原風險中立機率測度 5
2.3.1 無母數還原風險中立機率測度的方法 5
2.3.2 拉格朗日乘數法還原風險中立機率測度 7
2.4賽局理論之簡介 10
第三章 由選擇權市場價格還原風險中立機率測度 16
3.1 選擇權套利模型 16
3.2還原風險中立機率測度 22
3.3 考慮交易成本 23
第四章 實證分析 26
4.1 資料來源 26
4.2 實證方法與結果分析 26
4.2.1 套利機會的篩選 27
4.2.2 風險中立機率測度的型態 32
4.2.3市場上買權與賣權的價格合理性 35
第五章 結論 42
參考文獻 43		zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094751014en_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) 賽局理論zh_TW
dc.subject (關鍵詞) 線性規劃zh_TW
dc.title (題名) 應用賽局理論評價選擇權zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Black, F. and M. Scholes, 1973, The pricing of options and corporate liabilities. Journal of political Economy 81(3), 637-659.zh_TW
dc.relation.reference (參考文獻) Boyle, P. P. and T. Vorse, 1992, Option replication in discrete time with transaction cost. Journal of Finance 47(1), 271-294.zh_TW
dc.relation.reference (參考文獻) Cox, J. C., S. Ross, M. Rubinstein 1979, Option pricing: A simplified approach. Journal of Financial Economic 3,145-166.zh_TW
dc.relation.reference (參考文獻) Harrison, M. and D. Kreps, 1979, Martingale and arbitrage in multiperiod security markets. Journal of Economic Theory 20, 381-408.zh_TW
dc.relation.reference (參考文獻) Jackwerth, J. C., 2000, Recovering risk aversion from option prices and realized returns. The Review of Financial Studenies 13(2), 433-451.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) Kline, J., 2000, For the Student: Basic game theory. The Australian Economic Review 33(4), 381-387.zh_TW
dc.relation.reference (參考文獻) Leland, H., 1985. Option pricing and replication with transaction costs. Journal of finance 40(5), 1283-1301.zh_TW
dc.relation.reference (參考文獻) Melinkov A. A. and Y. G. Petrachenko, 2005, On option pricing in binomial market with transaction costs. Finance and Stochastics 9, 141-149.zh_TW
dc.relation.reference (參考文獻) Prasad C. and J. Somesh, 2001, Randomized stopping times and American option pricing with transaction costs. Mathematical Finance 11(1), 33-77.zh_TW
dc.relation.reference (參考文獻) Rubinstein, M., 1994, Implied Binomial Trees. Journal of Finance 49(3), 771-818.zh_TW
dc.relation.reference (參考文獻) Rubinstein, M. and J. Jackwerth, 1996, Recovering probability distributions from option prices. The Journal of Finance 51(5), 1611-1631.zh_TW
dc.relation.reference (參考文獻) Steven R., 2000, “Option exercise games: the intersection of real options and game theory. Journal of Applied Corporate Finance 13(2), 99-107.zh_TW
dc.relation.reference (參考文獻) Ales C., 2004, Mathematical Techniques in Finance. Tools for Incomplete Markets. Princeton University Press, New Jersey.zh_TW
dc.relation.reference (參考文獻) Neftci, S.N., 2004, An Introduction to the Mathematics of Financial Derivatives. Academic press, New York.zh_TW
dc.relation.reference (參考文獻) 張瓊芳，2005，由市場的選擇權價格還原風險中立機率分布，國立政治大學應用數學系碩士論文，台北。zh_TW
dc.relation.reference (參考文獻) 劉桂芳，2005，由選擇權市場價格建構具一致性之評價模型，國立政治大學應用數學系碩士論文，台北。zh_TW