政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32572
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 113648/144635 (79%)
Visitors : 51684690      Online Users : 578
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
    •  Adv. Search
    Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer Goto mobile version


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32572


    Title: 還原風險中立機率測度的雙目標規劃模型
    Recovering Risk-Neutral Probability via Biobjective Programming Model
    Authors: 廖彥茹
    Contributors: 劉明郎
    廖彥茹
    Keywords: 評價選擇權
    風險中立機率測度
    機率平賭測度
    非線性規劃
    option pricing
    risk-neutral probability measure
    martingale measure
    programming
    Date: 2005
    Issue Date: 2009-09-17 13:46:23 (UTC+8)
    Abstract: 本論文提出利用機率平賭性質由選擇權市場價格還原風險中立機率測度的雙目標規劃模型。假設對應同一標的資產且不同履約價的選擇權均為歐式選擇權，到期時標的資產的狀態為離散點且個數有限。若市場不存在套利機會時，建構出最小化離差總和及最大化平滑的雙目標規劃模型。將此雙目標規劃模型利用權重法轉換成單一目標之非線性模型，即可還原風險中立機率測度，並利用此風險中立機率測度評價選擇權的公平價格。最後，我們以台指選擇權(TXO)為例，驗證此模型的評價能力。
    This thesis proposes a biobjective nonlinear programming model to derive risk-neutral probability distribution of underlying asset. The method are used to choose probabilities that minimize the deviation between the observed price and the theoretical price as well as maximize the smoothness of the resulting probabilities. A weighting method is used to covert the model into a single objective model. Given a non-arbitrage observed option price, a risk-neutral probability distribution consistent with the observed option can be recovered by the model. This risk-neutral probability is then utilized to evaluate the fair price of options. Finally, an empirical study applying to Taiwan’s market is given to verify the pricing ability of this model.
    Reference: Adams K. J. and Van Deventer, “Fitting yield curve and forward rate curves with maximum smoothness”, Journal of Fixed Income 4, 52-62, 1994.
    Bachelier, L., “Theorie de la speculation”, Annales Sciences de L’Ecole Normale Superieure 17, 21-86, 1900.
    Black, F. and M. Scholes, “The pricing of options and corporate liabilities”, Journal of Political Economy 81, 637-659, 1973.
    Breeden, D. and R. Litzenberger, “Prices of State--Contingent Claims Implicit in Option Prices”, Journal of Business 51, 621-651, 1978.
    Brooke, A., D. Kendrick, and A. Meeraus, “GAMS - A user’s guide”, The Scientific Press, Reawood city, 1988.
    Buono, M., B. G.-A. Russell, and U. Yaari, “The efficacy of term structure estimation techniques: A Monte Carlo study”, Journal of Fixed Income 1, 52-59, 1992.
    A., “Mathematical techniques in finance”, Princeton University Press, 2004.
    Cox, J. and M. Rubinstein, “Option markets”, Prentice-Hall, 1985.
    Cox, J., S. Ross, and M. Rubinstein, “Option pricing: A simplified approach”, Journal of Financial Economics 7, 229-263, 1979.
    Francis, L., “Martingale restrictions tests of option pricing models”, working papers, University of California at Los Angeles, 1990.
    Garman, M. and S. Kohlhagen, "Foreign Currency Option Values", Journal of International Money and Finance 2, 231-37, 1983.
    Harrison, J. and D. M. Kreps, "Martingales and arbitrage in multiperiod securities markets", Journal of Economic Theory 20, 381-408, 1979.
    Harrison, J. and S. Pliska, “Martingales and stochastic integrals in the theory of continuous time trading”, Stochastic Processes and Their Applications 11, 215-260, 1981.
    Haugh, M., “Martingale pricing theory”, lecture note, Department of Industrial Engineering and Operation Research, Columbia University, 2004.
    Herzel, S., “Arbitrage opportunities on derivatives：A linear programming approach”, Dynamics of Continuous, Discrete and Impulsive System 12, 589-606, 2005.
    Ito, K., “On stochastic differential equation memories”, American Mathematical Society 4, 1-51, 1951.
    Jackwerth, J. C. and M. Rubinstein, “Recovering probability distributions from contemporaneous security prices”, working paper, University of California at Berkeley, 1995.
    Jackwerth, J. C. and M. Rubinstein, “Recovering probability distributions from option prices”, Journal of Finance 51, 1611-1632, 1996.
    Luenberger, D. G., “Linear and nonlinear programming”, 2nd edition, Addison-Wesley, 1984.
    MaCulloch, J., “The tax adjusted yield curve”, Journal of Finance 30, 811-829, 1975.
    Merton, R., “The theory of rational option pricing”, Bell Journal of Economics and Management Sciences 4, 141-183, 1973.
    Rubinstein, M., “Implied binomial trees”, Journal of Finance 49, 771-818, 1994.
    Shimko, D., “Bounds of probability”, RISK 6, 33-37, 1993.
    Siegel, S., “Nonparametric statistics”, McGraw-Hill, 1956.
    Vasicek, O. A. and H. G. Fong, “Term structure modeling using exponential splines”, Journal of Finance 37, 339-356, 1977.
    Wiener, N., “Differential-space”, J. Math. Phys., Mass. Inst. Technol. 2, 131-174, 1923.
    陳松男，金融工程學，華泰文化，2002。
    陳威光，選擇權：理論．實務與應用，智聖文化，2001。
    楊靜宜，選擇權策略的整數線性規劃模型，國立政治大學應用數學系碩士論文，2004。
    劉明郎、楊靜宜、劉宣谷，選擇權交易策略的整數線性規劃模型，第二屆台灣作業研究學會年會 暨作業研究理論與實務學術研討會，台北，2005。
    劉桂芳，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，2005。
    Description: 碩士
    國立政治大學
    應用數學研究所
    92751012
    94
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0092751012
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

    Files in This Item:

    File Description SizeFormat
    75101201.pdf38KbAdobe PDF2755View/Open
    75101202.pdf42KbAdobe PDF2755View/Open
    75101203.pdf75KbAdobe PDF2871View/Open
    75101204.pdf44KbAdobe PDF2738View/Open
    75101205.pdf44KbAdobe PDF2901View/Open
    75101206.pdf44KbAdobe PDF21639View/Open
    75101207.pdf104KbAdobe PDF26323View/Open
    75101208.pdf62KbAdobe PDF2852View/Open
    75101209.pdf110KbAdobe PDF2821View/Open
    75101210.pdf41KbAdobe PDF2718View/Open
    75101211.pdf50KbAdobe PDF2815View/Open
    75101212.pdf121KbAdobe PDF2940View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback