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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/32605
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/32605


    Title: 由選擇權市場價格建構具一致性之評價模型
    Building a Consistent Pricing Model from Observed Option Prices via Linear Programming
    Authors: 劉桂芳
    Liu, Kuei-fang
    Contributors: 劉明郎
    Liu, Ming-long
    劉桂芳
    Liu, Kuei-fang
    Keywords: 評價選擇權
    風險中立機率測度
    等價平賭測度
    線性規劃
    options pricing
    risk-neutral probability measure
    equivalent martingale measure
    linear programming
    Date: 2004
    Issue Date: 2009-09-17 13:50:05 (UTC+8)
    Abstract: 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。
    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.
    Reference: Black, F. and M. Scholes (1973), “Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81(3), 637-659.
    Churchill, R. V. (1963), “Fourier Series and Boundary Value Problems.” 2nd ed. New York, McGraw-Hill.
    Cox, J. and S. Ross (1976), “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics 3, 145-166.
    Cox, J., S. Ross, and M. Rubinstein (1979), “Option Pricing: A Simplified Approach.” Journal of Financial Economics 7(3), 229-263.
    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.
    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.
    Haugh, M. (2004), “Martingale Pricing Theory.” Lecture Note, Department of Industrial Engineering and Operation Research, Columbia University.
    Ito K. (1951), “On Stochastic Differential Equation Memories.” American Mathematical Society 4, 1-51.
    Jackwerth, J. (1997), “Generalized Binomial Trees.” Journal of Derivatives 5(2), 7-17.
    Jackwerth, J. (1999), “Option-Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review.” Journal of Derivatives 7(2), 66-82.
    King, A. (2002), “Duality and Martingale: A Stochastic Programming Perspective on Contingent Claims.” Mathematical Programming Ser. B 91, 543-562.
    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.
    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.
    Rubinstein, M. (1994), “Implied Binomial Trees.” Journal of Derivatives 49(3), 771-818.
    Sharpe, W. F. (1978), “Investments.” Prentice-Hall International.
    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.
    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。
    Description: 碩士
    國立政治大學
    應用數學研究所
    91751007
    93
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0917510071
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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