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研究生:李昀寰
研究生(外文):Yun-Huan Lee
論文名稱:隨機波動模型下自助法之應用
指導教授:樊采虹樊采虹引用關係
指導教授(外文):Tsai-Hung Fan
學位類別:博士
校院名稱:國立中央大學
系所名稱:統計研究所
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:2005
畢業學年度:93
語文別:中文
論文頁數:65
中文關鍵詞:自助法預測區間風險值厚尾分配隨機波動模型Black-Scholes 模型條件重點抽樣
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自 Black-Scholes 模型提出後,有關描述資產報酬之模型及相關問題即為一引人注目的研究課題。然而 Black-Scholes 模型中關於常數波動性及常態誤差的假設與實証結果並不吻合。實務模型中其分配函數尾端通常較常態模型厚,因此本文考慮隨機波動模型。我們的目標為計算在該模型下之風險值,並以自助法評價其估計量。
本文證明風險值估計量具有漸進常態性以及自助法的適當性。模擬結果顯示即使在誤差分配是自由度為 1 之下的 t 分配,對於參數估計與風險值估計均有不錯的結果。此外,我們應用參數自助法在隨機波動模型下建構預測區間,並以美國標準普爾 500 指數為例。結果顯示預測區間與實際資料的走勢一致。最後我們考慮在隨機波動模型下對於稀少事件的機率估計問題。本文提出以條件重點抽樣的概念估計此機率問題。模擬結果顯示條件重點抽樣估計量比蒙地卡羅估計量有較高的有效性,
也就是條件重點抽樣達到變異數降低的效果。
第一章 緒論.............1
1.1 研究動機.............1
1.2 研究背景.............3
1.3 研究方法.............5
第二章 隨機波動模型.............7
2.1 參數估計.............8
2.2 VaR 的估計.............11
2.3 自助法在參數與風險值之應用.............14
2.3.1 參數自助法.............15
2.3.2 非參數自助法.............15
2.4 數值模擬.............17
第三章 隨機波動模型下自助法預測區間.............31
3.1 預測區間的自助法演算法.............32
3.2 數值模擬與實例.............33
第四章 隨機波動模型之重點抽樣.............37
4.1 重點抽樣.............38
4.2 條件重點抽樣.............40
4.2.1 常態分配.............42
4.2.2 t 分配.............43
4.3 數值模擬.............46
第五章 結論.............50
參考文獻.............51
附錄一.............57
附錄二.............59
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