資產價格之雙變量機率分配預測

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郭建志(CHIEN-CHIH KUO) 查詢紙本館藏

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財務金融學系

論文名稱

資產價格之雙變量機率分配預測
(Bivariate Density Prediction for Financial Asset Prices)

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摘要(中)

本篇論文利用選擇權價格所提供的資訊，以兩種機率分配模型，混合型常態分配與廣義貝他分配，預估未來風險中立下的資產價格機率分配。在得到風險中立下的機率分配後，利用羃次效用函數將風險中立世界中的預測機率轉換為現實世界的預測機率分配，再使用四種關聯結構函數，高斯結構關聯函數、法蘭克結構關聯函數、干貝爾結構關聯函數與克萊頓結構關聯函數，將兩種資產的預測分配結合，轉換為雙變量的聯合分配。採用S&P 500與IBM在1996到2005年的選擇權價格資料進行模型的估計與關聯結構函數的結合，並以Berkowitz在2001年提出的統計檢定方法測試預測模型的預測能力。根據本論文的實證結果，以廣義貝他函數搭配克萊頓關聯結構函數的模型會有比較好的預測能力。

摘要(英)

Option prices provide a rich source of information for estimating risk-neutral world densities. This paper exploits lognormal mixture distribution and generalized beta distribution to forecast asset price risk-neutral probability distribution when options expire. The power utility function is used to estimate the risk aversion parameter, and transform the risk-neutral world density into the real world density. After completing transformation, four kinds of copula functions, including Gassian copula, Frank copula, Gumbel copula and Clayton copula are used to combined two predictive density. The empirical results are examined with test of Berkowitz (2001). According to the empirical results, the combination of generalized beta distribution and Clayton copula outperforms other models in this paper.

關鍵字(中)

★ 現實世界機率分配
★ 風險中立機率分配
★ 關聯結構函數
★ 廣義貝他分配
★ 混合型對數常態分配

關鍵字(英)

★ lognormal mixture
★ generalized beta distribution

論文目次

第一章、緒論 1
1-1 研究動機與目的 1
1-2 研究架構 1
第二章、文章回顧 2
2-1 無風險世界中的機率模型 2
2-2 風險轉換 3
第三章、風險轉換方法與關聯結購函數 4
3-1 風險中立(risk-neutral world)下的機率分配 4
3-2 現實世界(real world)的機率分配 4
3-3 關聯結構函數(copula) 5
第四章、機率分配估計方法(density estimation methods) 7
4-1 機率測度轉換 7
4-2 混合型對數常態分配(mixtures of lognormal densities, MLN) 7
4-3 廣義貝他分配(generalized beta densities, GB2) 9
4-4 風險中立下機率分配的參數估計 11
4-5 風險中立世界到現實世界轉換過程的參數估計 11
4-6 關聯結構函數選用 12
4-7 關聯結構函數的參數估計 14
第五章、資料來源 15
第六章、實證結果 15
6-1 單變量機率分配預測 15
6-2 雙變量機率分配預測 20
第七章、結論 22
參考文獻 23

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指導教授

王耀輝(Yaw-Huei Wang)

審核日期

2007-7-17

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