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    題名: 由市場的選擇權價格還原風險中立機率分布
    作者: 張瓊方
    Chang, Chiung-Fang
    貢獻者: 劉明郎
    張瓊方
    Chang, Chiung-Fang
    關鍵詞: 選擇權交易策略
    線性規劃
    套利機會
    風險中立機率測度
    選擇權評價公式
    option trading strategy
    linear programming
    arbitrage opportunity
    risk-neutral probability
    option pricing formula
    日期: 2005
    上傳時間: 2009-09-17 13:49:59 (UTC+8)
    摘要: 本論文提出線性規劃的方法以還原隱藏於選擇權市場價格中的風險中立機率測度，並利用該機率測度計算選擇權的合理價格。模型中假設選擇權對應同一標的資產與到期日，資產價格於到期日的狀態為離散點且個數有限，當市場不具任何套利機會時，以極小化市場價格與合理價格之離差總和作為挑選風險中立機率測度的準則。最後，以臺指選擇權(TXO)的交易資料做為實證對象。實證中發現，加入平滑限制式與離差權重之線性規劃模型在評價歐式選擇權合理價格的效能最為優異。
    The thesis proposes a liner programming to recover the risk-neutral probability distribution of an underlying asset price from its associated market option prices, and we evaluate the fair prices of options via the resulting risk-neutral probability distribution. Assume that we face a series of European options with different exercise prices on the same maturity and underlying asset in this linear programming model. The criterion of choosing a risk-neutral probability distribution is minimizing the sum of total deviations subject to requiring that the fair prices of options are consistent with observed market option prices. Finally, we take the trading data of TXO as an empirical study. The empirical study indicates that the model with smooth constraints and weighted deviations has the best performance in pricing the rational price of European options.
    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.
    Breeden, D.T. and R.H. Litzenberger (1978), "Prices of State Contingent Claims Implicit in Option Prices." Journal of Business 51, 621-652.
    Brooke, A., D. Kendrick, and A. Meeraus (1988), GAMS - A User’s Guide, The Scientific Press, Redwood City, CA.
    Černý, A. (2004), Mathematical Techniques in Finance: Tools for Incomplete Markets, Princeton University Press, Imperial College London.
    Cox, J. and S. Ross (1976), "The Valuation of Options for Alternative Stochastic Process." Journal of Financial Economics 3, 145-166.
    Cox, J. and S. Ross and M. Rubinstein (1979), "Option Pricing: A Simplified Approach." Journal of Financial Economics 7(3), 229-263.
    CPLEX Optimization, Inc. (1993), Using the CPLEX Callable Library and CPLEX Mixed Integer Library, Incline Village, NY.
    GAMS Development Corporation (2003), GAMS - The Solver Manual, Washington, DC.
    Harrison, J. and D. Kerps (1979), "Martingales and Multiperiod Securities Markets." Journal of Ecnomic Theory 20, 381-408.
    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.
    Ito, K. (1951), "On Stochastic Differencial Equation Memories." American Mathematical Society 4, 1-51.
    Merton, R. C. (1973), "Theory of Rational Option Pricing." Bell Journal of Economics and Management Science 4, Spring, 141-183.
    Merton, R. C., M. S. Scholes, and M. L. Gladstein (1978), "The Returns and Risk of Alternative Call Option Portfolio Strategies." Journal of Business 51, 183-241.
    Papahristodoulou, C. (2004), "Option Strategies with Linear Programming." European Journal of Operational Research 157, 246-256.
    Prisman, E. Z., "Valuation of Risky Assets in Arbitrage-Free Economies with Frictions." The Journal of Finance 41(3), 293-305.
    Rendleman, R. J. (1995), "An LP Approach to Option Portfolio Selection." Advances in Futures and Options Research 8, 31-52.
    Rubinstein, M. and J. Jackwerth (1996), "Recovering Probability Distributions from Option Prices." The Journal of Finance 51(5),1611-1631.
    Rubinstein, M. (1994), "Implied Binomial Trees." Journal of Finance 49(3), 771-818.
    Herzel, S. (2005), "Arbitrage Opportunities on Derivatives: a Linear Programming Approach." Dynamics of Continuous, Discrete, and Impulsive Systems, Series B: Applications and Algorithms 12(4), 589-606.
    謝劍平 (2000)，現代投資學，智勝文化。
    陳松男 (2003)，基礎選擇權與期貨，新陸書局。
    楊靜宜 (2004)，選擇權交易策略的整數線性規劃模型，政治大學應用數學系碩士論文。
    劉桂芳 (2005)，由選擇權市場價格建構具一致性之評價模型－使用線性規劃，政治大學應用數學系碩士論文。
    描述: 碩士
    國立政治大學
    應用數學研究所
    91751005
    94
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0917510051
    資料類型: thesis
    顯示於類別:[應用數學系] 學位論文

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