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研究生:黃柳月
研究生(外文):Liu-Yuen Huang
論文名稱:對財務時間序列資料配適厚尾分佈
論文名稱(外文):Fitting financial time series data to heavy tailed distribution
指導教授:郭美惠郭美惠引用關係
指導教授(外文):Mei-Hui Guo
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
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:51
中文關鍵詞:股價波動率Pearson type VII厚尾分佈StableVaRPearson type IV
外文關鍵詞:VaRPearson type IVStablePearson type VIIvolatilityheavy tailed
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一般財經資料具有厚尾及偏斜的特性,以往研究者常會使用Stable分佈來配適厚尾分佈.在此篇文章中,收集美國電腦科技股及金融保險股這兩類股票中的七家廠商,分別對每日對數報酬率及每月對數報酬率這兩種時間序列資料配適三種厚尾分佈,分別為Pearson type IV,Pearson type VII與Stable分佈.
在文中比較其配適狀況,並將其應用在財務上風險值VaR與股價波動率的計算,且進一步探討選擇權市場定價理論與微笑波幅.



Financial data, such as daily or monthly maximum log return of stock price usually possess heavy tail and skewness properties. In this thesis, we consider stock price data of computer hardware and money center banks. Heavy-tailed distributions including Pearson type IV, Pearson type VII and stable distribution were fitted to the daily log return of the data sets, and goodness of fit were compared. For the monthly
maximum log return, nonlinear threshold time series models were fitted with heavy tailed innovation distributions. In addition, the value at risk and volatility of the data sets are derived from the fitted distributions.



1.緒論
2.文獻探討
2.1 Pearson type IV分佈與Pearson type VII分佈
2.2 Stable分佈
2.3 非線性自我迴歸模型:門檻自我迴歸模型
2.4 選擇權評價模式:Black-Scholes Model
2.5 隱含波幅
3.實證結果與分析
3.1 每日對數報酬率的資料分析
3.2 每月最大報酬率的資料分析
4.財務上的應用
4.1 應用每日對數報酬率資料計算VaR與股價波動率
4.2 應用每月最大對數報酬率資料計算每日對數報酬率的VaR
5.結論與建議
References



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4. Hull, J.C.(1997), Options, Futures, & Other Derivatives, 4th ed. Pretice-Hall International, Inc.
5. Kendall, M.G. and Alan Stuart(1977), The advanced theory of Statistics. Vol 1: Distribution theory, 4th ed, ch6.
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16. 李伶芳(2001), 應用具有厚尾誤差項的非線性自我迴歸模型計算風險值.

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