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研究生:謝盈弘
論文名稱:馬可夫鏈蒙地卡羅法在外匯選擇權定價的應用
指導教授:杜化宇杜化宇引用關係陳麗霞陳麗霞引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:64
中文關鍵詞:馬可夫鏈蒙地卡羅法外匯選擇權貝氏選擇權評價
外文關鍵詞:MCMCRegime switchingRegime changeGibbs Samplingcurrency optionMarkov Chain Monte Carlo
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本篇論文以Regime Switching Stochastic Volatility (RSV) 作為外匯選擇權市場的的波動度模型,採用馬可夫鏈蒙地卡羅法 ( Markov Chain Monte Carlo ) 中的Gibbs Sampling演算法估計RSV模型的參數,並預測外匯選擇權在RSV模型下的價格。
數值結果方面首先對Gibbs Sampling參數估計的結果做討論,再對預測出的選擇權價格與Black and Scholes作比較,最後並提出笑狀波幅與隱含波動度平面的結果。
本研究所得到之結論:
1. RSV模型與MCMC模擬法的組合,具備產生笑狀波幅的能力,提供足夠證據顯示,RSV模型與MCMC演算法所計算出來的選擇權價格,確實反應且捕捉到了市場上選擇權價格所應具備的特色。
2. 本模型能有效解釋期限結構 (Term Structure of Volatility) 、笑狀波幅 (Volatility Smile) 的現象。
關鍵字:
馬可夫鏈蒙地卡羅法、外匯選擇權、貝氏選擇權評價、MCMC、Regime switching、Regime change、Gibbs Sampling、currency option、Markov Chain Monte Carlo
第一章 緒論...1
第一節 研究動機與目的...1
第二節 研究方法與限制...3
第三節 研究架構.........4
第二章 理論與文獻.......6
第一節 笑狀波幅、期限結構與隱含分配...6
第二節 隨機波動模型與估計方法........11
第三節 Bollen五元樹..................17
第四節 貝氏選擇權評價相關文獻........23
第三章 研究方法......................23
第一節 資料選取與軟體說明
第二節 Regime Switching Stochastic Volatility Model模型建構與
定義變數......................23
第三節 馬可夫鏈蒙地卡羅法............25
第四節 預測外選擇權的價格及其演算法的建構...30
第四章 結果分析.............................36
第一節 Gibbs Sampling抽樣結果...............44
第二節 外匯選擇權價格模擬結果...............44
第二節 笑狀波幅與隱含波動度平面.............48
第五章 結論與後續研究建議...................51
第一節 結論.................................55
第二節 後續研究建議.........................57
參考文獻.....................................59
圖次
圖 1-1 本文研究架構流程...................5
圖 2-1 四元樹............................17
圖 2-2 五元樹跳動幅度....................18
圖 2-3 五元樹............................18
圖 3-1 匯率每周收盤價(美分)..............24
圖 3-2 每周匯率收盤價之對數報酬率........24
圖 3-3 蒙地卡羅法堆疊....................42
圖 4-1 Gibbs Sampling 疊代次數與參數值...46
圖 4-2 參數之邊際後驗分配(Marginal Posterior Distribution )............................47
圖 4-3 外匯選擇權價格模擬................50
圖 4-4 外匯選擇權價格模擬之分配..........50
圖 4-5 隱含波動度平面....................52
圖 4-6 笑狀波福..........................53
圖 4-7 Bollen五元樹堆疊..................56
表次
表 1 Gibbs Sampling參數估計結果...........45
表 2 外匯選擇權價格模擬結果...............49
演算法
演算法 1 決定Bollen五元樹中五個分枝的機率.....20
演算法 2 Gibbs Sampling演算法.................32
演算法 3 預測外匯選擇權的價格.................43
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陳松男,金融工程學.,民國九十一年,華泰書局。
陳威光,選擇權:理論、實務與應用.,民國八十九年,智勝文化。
黃大展 (2001),隨機波動下的二元樹狀模型之探討. 國立政治大學財務管理學系未出版碩士論文,民國九十年六月。
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