門檻隨機波動模型下風險值之經驗貝氏分析

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王義富(Yi-Fu Wang) 查詢紙本館藏

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統計研究所

論文名稱

門檻隨機波動模型下風險值之經驗貝氏分析
(Empirical Bayesian Analysis on the Value at Risk of Threshold Stochastic Volatility Models.)

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摘要(中)

近年來，由於經濟市場的快速成長，使得投資組合愈來愈受到重視。在實務上，往往利用具時間序列的模型來對股價進行模型配適，以達到預測的效果。但由於現今經濟市場存在太多影響因素，因此學者們紛紛提出許多的模型來配適股價的動態，而隨機波動模型與門檻隨機波動模型為兩種近來常被討論的模型。
本文以門檻隨機波動模型，利用經驗貝氏方法建立經驗貝氏模型，其動機在於當資料來源無法在上述兩模型間做一確認時，經驗貝氏模型可做為一折衷。另外也考慮風險值 (VaR) 之預測，分別對隨機波動模型、門檻隨機波動模型及經驗貝氏模型進行比較。結果顯示經驗貝氏模型不僅具有較穩健的預測能力，也大大的降低了選模錯誤的風險。

關鍵字(中)

★ 風險值
★ 經驗貝氏
★ 隨機波動模型
★ 門檻隨機波動模型

關鍵字(英)

論文目次

第一章緒論 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥01
1.1 研究背景與動機 ‥‥‥‥‥‥‥‥‥‥01
1.2 研究目的與方法 ‥‥‥‥‥‥‥‥‥‥07
1.3 研究架構 ‥‥‥‥‥‥‥‥‥‥‥‥‥09
第二章隨機波動模型之貝氏推論 ‥‥‥10
2.1 隨機波動模型 ‥‥‥‥‥‥‥‥‥‥‥10
2.2 參數之貝氏估計 ‥‥‥‥‥‥‥‥‥‥11
2.2.1 吉布斯抽樣‥‥‥‥‥‥‥‥‥‥14
2.3 風險值之估計 ‥‥‥‥‥‥‥‥‥‥‥20
第三章門檻隨機波動模型之貝氏推論‧25
3.1 門檻隨機波動模型 ‥‥‥‥‥‥‥‥‥25
3.2 參數之貝氏估計 ‥‥‥‥‥‥‥‥‥‥27
3.2.1 吉布斯抽樣 ‥‥‥‥‥‥‥‥‥29
3.3 風險值之估計 ‥‥‥‥‥‥‥‥‥‥‥34
第四章經驗貝氏模型 ‥‥‥‥‥‥‥‥‥36
4.1 經驗貝氏模型 ‥‥‥‥‥‥‥‥‥‥‥38
4.2 超參數之估計 ‥‥‥‥‥‥‥‥‥‥‥39
4.3 參數之經驗貝氏估計 ‥‥‥‥‥‥‥‥42
4.4 風險值之估計 ‥‥‥‥‥‥‥‥‥‥‥43
第五章模擬研究 ‥‥‥‥‥‥‥‥‥‥‥44
5.1 隨機波動模型 ‥‥‥‥‥‥‥‥‥‥‥44
5.2 門檻隨機波動模型 ‥‥‥‥‥‥‥‥‥45
5.3 經驗貝氏模型 ‥‥‥‥‥‥‥‥‥‥‥46
5.4 模型比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥47
5.5 貝氏風險 ‥‥‥‥‥‥‥‥‥‥‥‥‥50
5.5.1 隨機波動模型之資料 ‥‥‥‥‥‥51
5.5.2 門檻隨機波動模型之資料 ‥‥‥‥54
5.6 實例分析 ‥‥‥‥‥‥‥‥‥‥‥‥‥55
第六章結論 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥73
參考文獻 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥75

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2005-7-11

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