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| 研究生： |
張瓊方 Chang, Chiung-Fang |
|---|---|
| 論文名稱： |
由市場的選擇權價格還原風險中立機率分布 |
| 指導教授： | 劉明郎 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2006 |
| 畢業學年度： | 94 |
| 語文別： | 中文 |
| 論文頁數： | 49 |
| 中文關鍵詞： | 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 |
| 外文關鍵詞： | option trading strategy, linear programming, arbitrage opportunity, risk-neutral probability, option pricing formula |
| 相關次數： | 點閱：81 下載：70 |
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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.
摘要..................................................iii
ABSTRACT...............................................iv
表目錄.................................................vi
圖目錄................................................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
第三章選擇權評價理論與無套利機會之檢測..................6
3.1 選擇權評價理論..................................6
3.1.1 Black-Scholes歐式選擇權評價模型...........6
3.1.2 平賭過程評價方法...........................8
3.2 還原風險中立機率測度法則.......................11
3.2.1 無母數還原風險中立機率測度法..............11
3.2.2 還原風險中立機率測度之線性規劃模型........13
3.3 無套利機會之檢測法..............................17
第四章 由選擇權市場價格還原風險中立機率測度模型........22
第五章 實證分析........................................26
5.1 實證資料來源與選取.............................26
5.2 實證結果分析...................................27
5.3 平滑風險中立機率測度曲線.....................29
5.3.1 直觀法修正風險中立機率測度之曲線..........29
5.3.2 考慮相鄰三點間的機率限制..................31
5.3.3 考慮成交量之影響..........................33
第六章 結論............................................46
參考文獻...............................................47
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