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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/32572


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    題名: 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
    作者: 廖彥茹
    貢獻者: 劉明郎
    廖彥茹
    關鍵詞: 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
    日期: 2005
    上傳時間: 2009-09-17 13:46:23 (UTC+8)
    摘要: 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.
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    陳松男，金融工程學，華泰文化，2002。
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    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。
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    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。
    描述: 碩士
    國立政治大學
    應用數學研究所
    92751012
    94
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0092751012
    資料類型: thesis
    顯示於類別:[應用數學系] 學位論文

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