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系統識別號 U0002-1101200712485400
中文論文名稱 風險值衡量與風險值避險法
英文論文名稱 Value-at-Risk Measures and Value-at-Risk based Hedging Approach
校院名稱 淡江大學
系所名稱(中) 財務金融學系博士班
系所名稱(英) Department of Banking and Finance
學年度 95
學期 1
出版年 96
研究生中文姓名 洪瑞成
研究生英文姓名 Jui-Cheng Hung
學號 891490053
學位類別 博士
語文別 英文
口試日期 2006-12-30
論文頁數 84頁
口試委員 指導教授-邱建良
共同指導教授-李命志
委員-俞海琴
委員-邱建良
委員-莊武仁
委員-張倉耀
委員-聶建中
委員-王凱立
中文關鍵字 風險值  跳躍  絕對風險值避險比率  雙變量馬可夫狀態轉換模型  多期絕對風險值避險比率  最小變異避險比率 
英文關鍵字 Value-at-Risk  Jump  zero-VaR hedge ratio  Bivariate Markov regime switching model  Multi-period zero-VaR hedge ratios  Minimum hedge ratios 
學科別分類 學科別社會科學商學
中文摘要 本論文著重在風險值的衡量與以風險值為基礎的避險比率上,共包含三個部份,分別為「在動態跳躍與訊息不對稱下的風險值計算」、「絕對風險值避險比率」與「以雙變量馬可夫狀態轉換模型估計多期的絕對風險值避險比率與最小變異避險比率」。
將此三部份的內容簡敘如下。第一部分使用GARJI、ARJI與不對稱GARCH等三個模型在估計一天的相對風險值之績效。本文使用此三個模型計算兩個股價指數(道瓊指數與S&P 500指數)與一個匯率(日圓)的多部位風險值,其用意在於探討價格跳躍與訊息不對稱效果對於衡量風險值績效的影響。實證結果發現,在資產報酬率具有隨時間變動的跳躍現象以及訊息不對稱的效果下,由GARJI與ARJI模型所估算出來的風險值無論信心水準的高低,均能提供令人信賴的準確度。另外,由MRSB顯示,GARJI所估算出的風險值最具效率性。
第二部份本文以風險值為基礎,推出以絕對風險值為目標函數的絕對風險值避險比率。當期貨報酬率服從單純平賭過程或是風險趨避程度趨於無窮大的條件下,絕對風險值避險比率將縮減成為最小變異避險比率。於實證過程中,本文採用包含誤差修正項的雙變量固定相關係數GARCH(1,1)模型估計計算最小變異避險比率所需的參數,並且比較其與Hsin et al. (1994)所提出的以極大化效用函數為目標的避險比率。
第三部份本文推廣單期的絕對風險值避險比率(Hung et al., 2006)成為多期的情況,並使用四狀態雙變量馬可夫轉換模型和雙變量對角化VECH GARCH(1,1)模型估計道瓊指數與S&P 500的絕對風險值避險比率與最小變異避險比率。與Bollen et al. (2000)不同之處在於,本文分別從樣本內與樣本外避險績效的角度,探討在雙變量的情況下,狀態轉換與GARCH這兩種方法何者對於樣本內的配適度以及樣本外的變異數預測較佳。實證結果顯示狀態轉換的方式提供較佳的樣本內配適度;然而,於大多數的情況下,GARCH在樣本外的變異數預測上較具有優勢。
英文摘要 This study focuses on VaR measurement and VaR-based hedge ratio, and it contains three parts. The first part is titled “Estimation of Value-at-Risk under Jump Dynamics and Asymmetric Information”, the second part is named “Hedging with Zero-Value at Risk Hedge Ratio”, and the last one is “Bivariate Markov Regime Switching Model for Estimating Multi-period zero-VaR Hedge Ratios and Minimum Variance Hedge Ratios”.
A brief introduction of these three parts is described as follow: The first part employs GARJI, ARJI and asymmetric GARCH models to estimate the one-step-ahead relative VaR and compare their performances among these three models. Two stock indices (Dow Jones industry index and S&P 500 index) and one exchange rate (Japanese yen) are used to estimate the model-based VaR, and we investigate the influences of price jumps and asymmetric information on the performance of VaR measurement. The empirical results demonstrate that, while asset returns exhibited time-varying jump and the information asymmetric effect, the GARJI-based and ARJI-based VaR provide reliable accuracy at both low and high confidence levels. Moreover, as MRSB indicates, the GARJI model is more efficient than alternatives.
In the second part, a mean-risk hedge ratio is derived on the foundation of Value-at-Risk. The proposed zero-VaR hedge ratio converges to the MV hedge ratio under a pure martingale process or an infinite risk-averse level. In empirical section, a bivariate constant correlation GARCH(1,1) model with an error correction term is adopted to calculate zero-VaR hedge ratio, and we compare it with the one proposed by Hsin et al. (1994) which maximized the utility function as their objective.
The last part extends one period zero-VaR hedge ratio (Hung et al., 2006) to the multi-period case, and also employed a four-regime bivariate Markov regime switching model and diagonal VECH GARCH(1,1) model to estimate both zero-VaR and MV hedge ratios for Dow Jones and S&P 500 stock indices. Dissimilar with Bollen et al. (2000), the in-sample fitting abilities and out-of-sample variance forecasts between regime-switching and GARCH approaches are investigated in a bivariate case through in- and out-of-sample hedging performances. The empirical evidences show that the regime switching approach provides better in-sample fitting ability; however, GARCH approach has better out-of-sample variance forecast ability for most cases.
論文目次 TABLE OF CONTENTS
Page
ACKNOWLEDGEMENT ii
ABSTRACT IN CHINESE iii
ABSTRACT IN ENGLISH iv
LIST OF TABLES ix
LIST OF FIGURES x

PART I 1
Estimation of Value-at-Risk under Jump Dynamics and Asymmetric Information
ABSTRACT 2
CHAPTER
1. Introduction 3
1.1 Motivations and Objectives 3
1.2 Flow Chart 5
2. Literature Review 6
3. Model-based VaR Estimates and Evaluation Methods 8
3.1 VaR Definition 8
3.2 Evaluation Methods 9
3.2.1 General Loss Functions 9
3.2.2 Binary Loss Function 9
3.2.3 Quadratic Loss Function 10
3.2.4 Likelihood Ratio Tests 10
3.2.5 Mean Relative Scaled Bias 11
4. Econometric Methodology 12
4.1 GARJI Model 12
4.2 Asymmetric GARCH Model 15
5. Empirical Results and Analysis 17
5.1 Data Description and Preliminary Analysis 17
5.2 Empirical Results and Analysis 17
5.2.1 Estimation and Analytical Computation of Model-based VaR 17
5.2.2 Prediction Performance of the Model-based VaR 22
6. Conclusions 27
BIBLIOGRAPHY 28

PART II 30
Hedging with Zero-Value at Risk Hedge Ratio
ABSTRACT 31
CHAPTER
1. Introduction 32
1.1 Motivations and Objectives 32
1.2 Flow Chart 34
2. Literature Review of The Hedge Ratios 35
3. The Derivation of Zero-VaR Hedge Ratio 38
4. Econometric Methodology 42
4.1 Bivariate Constant-Correlation GARCH Model 42
4.2 Evaluation of Hedging Effectiveness 44
5. Empirical Results 45
5.1 Data Description 45
5.2 Empirical Results 46
6. Conclusions 53
BIBLIOGRAPHY 54
Appendix A 57
Appendix B 58

PART III 59
Bivariate Markov Regime Switching Model for Estimating Multi-period zero-VaR Hedge Ratios and Minimum Variance Hedge Ratios
ABSTRACT 60
CHAPTER
1. Introduction 61
1.1 Motivations and Objectives 61
1.2 Flow Chart 64
2. Multi-period Zero-VaR Hedge Ratio 65
2.1 Derivation of Multi-period Zero-VaR hedge ratio 65
2.2 Relationship Between Multi-period Zero-VaR Hedge Ratios and Risk-
averse Level 66
2.3 Relationship Between Multi-period Zero-VaR Hedge Ratios and Hedging Horizon 66
3. Econometric Methodology 68
3.1 Four-regime Bivariate Markov Switching Model 68
3.2 The Diagonal VECH GARCH Model 71
3.3 Evaluation of Hedging Performance 72
4. Empirical Results 74
4.1 Data Description 74
4.2 Empirical Results 75
4.2.1 Estimation of Four-regime Bivariate Markov Switching Model 75
4.2.2 Estimation of Diagonal VECH GARCH(1,1) Model 78
4.2.3 In- and Out-of-sample Hedging Performance 79
5. Conclusions 82
BIBLIOGRAPHY 83



LIST OF TABLES
Page
PART I
Table 1. Descriptive statistics of daily return 17
Table 2. Estimation results of GARJI model 18
Table 3. Estimation results of ARJI model 19
Table 4. Estimation results of asymmetric GARCH model 20
Table 5. Forecasting performance summary for different VaR models at 95%
confidence level 23
Table 6. Forecasting performance summary for different VaR models at 99%
confidence level 24
Table 7. Forecasting performance summary for different VaR models at 99.5%
confidence level 25
Table 8. Forecasting performance summary for different VaR models at 99.9%
confidence level 26

PART II
Table 1. Summary statistics of the spot and futures returns of S&P 500 45
Table 2. Bivariate constant correlation GARCH(1,1) model 47
Table 3. HKL and zero-VaR hedge ratios for different risk-averse levels 51
Table 4. Comparison of within-sample hedging effectiveness 52

PART III
Table 1. Summary statistics of the spot and futures returns for daily stock indices 74
Table 2. Estimation results of four-regime bivariate Markov switching model 76
Table 3. Estimation results of diagonal VECH GARCH(1,1) model 79
Table 4. Comparison of hedging performance 81




LIST OF FIGURES
Page
PART I

Figure 1. Conditional jump intensity for Dow Jones industry index 21
Figure 2. Conditional jump intensity for S&P 500 22
Figure 3. Conditional Jump Intensity for Japanese yen 22

PART II
Figure 1. MV hedge ratio and zero-VaR hedge ratio 48
Figure 2. Comparison of MV, HKL2.5, and zero-VaR75% hedge ratios 50

PART III
Figure 1. The relationship between multi-period zero-VaR hedge ratio and risk-averse
level 67
Figure 2. The relationship between multi-period zero-VaR hedge ratio and hedging
horizon 67
Figure 3. Ex-post probabilities of high variance regime for spot and futures of Dow Jones 77
Figure 4. Ex-post probabilities of high variance regime for spot and futures of S&P 500. 78
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