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研究生:陳律延
研究生(外文):Lu Yen Chen
論文名稱:不對稱馬可夫狀態轉換GARCH模型在台指選擇權評價的應用
論文名稱(外文):Markov Regime-Switching Asymmetric GARCH model and Evaluation of TXO
指導教授:徐憶文徐憶文引用關係
指導教授(外文):Y. W. Shyu
學位類別:碩士
校院名稱:長庚大學
系所名稱:企業管理研究所
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2008
畢業學年度:97
論文頁數:119
中文關鍵詞:Black-Scholes選擇權評價模型Markov Regime-Switching GARCH model
外文關鍵詞:B-S modelMarkov Regime-Switching GARCH model
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本研究引進添加了馬可夫狀態轉換參數的MRS-GARCH系列模型(MRS-GARCH、MRS-EGARCH、MRS-GJR-GARCH),與傳統波動性模型(歷史波動度、GARCH、EGARCH、GJR-GARCH)做對照,先觀察它們對於台股指數報酬率的配適度,再比較它們搭配Black-Scholes選擇權評價模型時,對台指選擇權價格的預測能力。
由於股市報酬分配常有厚尾高狹峰的現象,我們也放寬傳統迴歸模型之誤差項條件分配服從常態的假設,使其服從t分配或一般化誤差分配(GED),並使自由度可隨不同的狀態做切換,冀其也能描繪不同狀態下誤差分配的峰態,增進模型的配適度與預測力。
模型的配適度將用最大概似函數值、AIC、SBC等準則作比較,而模型預測力的指標將採用統計漏失函數。最後,為了統計嚴謹性起見,我們將使用無母數Wilcoxon符號等級檢定來判定某模型的預測誤差是否有顯著小於其他模型的預測誤差。
實證結果顯示,MRS-GARCH系列模型的確能有效降低波動度與台指買權價格預測的誤差,無論是台指報酬率的描繪或者波動度之動態的捕捉,還是配合B-S模型預測價格的能力,都有顯著的提升。
In this paper we compare the classic Generalized Autoregressive Conditional Heteroscedasticity models with the ones linked Markov Regime switching model together in terms of their goodness of fit of TAIEX and forecastability of price of TXO by B-S model.
Not only normal but also fat-tailed leptokurtic conditional distributions for the innovations are assumed, and the degrees of freedom can switch between the different regimes to draw time-varying kurtosis.
The goodness of fit of the competing models are evaluated with the value of maximum likelihood function, AIC, and SBC. However, the forecasting performances of them are measured by the statistical loss functions. To obtain an official outcome on statistic, we apply nonparametric Wilcoxon signed rank test to ensure some model is significantly better than the others.
The empirical result demonstrates that MRS-GARCH family do overall outperform GARCH family in fitting TAIEX, forecasting volatility, and reducing the inaccuracy of the evaluation of TXO in B-S option pricing model.
指導教授推薦書…………………………………………………………
口試委員會審定書………………………………………………………
授權書…………………………………………………………………iii
誌謝……………………………………………………………………iv
中文摘要…………………………………………………………………v
英文摘要………………………………………………………………vi
目錄……………………………………………………………………vii
第一章 緒論……………………………………………………………1
第一節 研究背景與動機…………………………………………1
第二節 研究目的…………………………………………………4
第三節 研究架構…………………………………………………6
第二章 文獻探討………………………………………………………7
第一節 波動模型與誤差項分配…………………………………7
第二節 狀態轉換模型……………………………………………15
第三節 狀態轉換與波動模型在選擇權評價的應用……………24
第三章 研究方法………………………………………………………26
第一節 研究流程…………………………………………………26
第二節 資料來源與應用軟體……………………………………27
第三節 Black-Scholes選擇權評價模式…………………………31
第四節 波動性模型………………………………………………33
第五節 預測力的衡量方法與顯著性檢定………………………45
第四章 實證分析………………………………………………………48
第一節 台灣股價指數報酬率分析………………………………48
第二節 波動性模型參數估計結果……………………………53
第三節 配適度與預測力分析……………………………………62
第五章 結論…………………………………………………………72
參考文獻………………………………………………………………75
附錄A…………………………………………………………………83
附錄B…………………………………………………………………108

圖 目 錄
圖 3-2-1 台灣證券交易所發行量加權股價指數走勢………………29
圖 4-1-1 台灣證券交易所發行量加權股價指數報酬率……………48
圖 4-1-2 Jarque-Bera 統計量與其他敘述統計量…………………50

表 目 錄
表 3-2-1 Bakshi, Cao, and Chen(1997)的買權Moneyness…………28
表 4-2-1 GARCH系列波動性模型參數之估計值及其標準誤……54
表 4-2-2 MRS-GARCH參數之估計值及其標準誤…………………59
表 4-2-3 MRS-EGARCH參數之估計值及其標準誤………………60
表 4-2-4 MRS-GJR-GARCH參數之估計值及其標準誤…………61
表 4-3-1 各模型之AIC、SBC、LLF與排名…………………………63
表 4-3-2 波動度預測力之統計漏失函數排名………………………65
表 4-3-3 買權價格預測力之統計漏失函數排名……………………68
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7. 陳煒朋,〈GARCH模型與隱含波動性模型預測能力之比較〉,淡江大學財務金融研究所,1999。
8. 林佩蓉,〈Black-Scholes模型在不同波動性衡量下之表現-股價指數選擇權〉,東華大學企業管理研究所,2002年。
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10. 楊亦農,《時間序列分析:經濟與財務上之應用》,台北市,雙葉書廊,2006年。
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