風險之衡量與預測為財務上重要的課題，但多數文獻皆集中探討金融商品上之風險與預測，對於能源商品之探討相對較為缺乏。然而受到供需不均、國際石油輸出組織政策及政治面干涉等因素影響，原油市場的價格波動極大，油價持續向上攀升，不僅對原油市場的交易造成影響，金融市場亦間接受到不小衝擊。有鑑於原油市場價格之高度波動性，因此探討原油商品的風險亦為重要的課題。本文除修正傳統方法在衡量與預測上之不足，更進一步研究與分析西德州(West Texas Intermediate, WTI)原油商品之風險值、跳躍波動以及在預測上所面臨的問題。 
第一個主題探討風險值。風險值是財務上最為廣泛用來估計風險的指標，本文採用RiskMetrics及AR-GARCH兩模型估計原油之風險值，結合移動視窗(rolling window)與拔靴法(bootstrapping)的方法進行估計。拔靴法解決了蒙地卡羅模擬法需要設定分配的假設及使用歷史模擬法恐有樣本資料不足的情形，因此晚近研究均以拔靴法取代財務上過去常用之蒙地卡羅模擬法與歷史模擬法。拔靴法的結果顯示在「估計期間外一天的預測 (one-day-ahead forecast)」風險值預測表現較佳，但「估計期間外十天的預測(ten-days-ahead forecast)」表現則不盡理想。另外，使用RiskMetrics或是AR-GARCH模型估計之預測績效差異不大。
第二個主題探討加入跳躍值來衡量原油與汽油之波動性。傳統模型多建立在連續且平穩的擴散過程上，一旦有異常事件發生，價格產生劇烈波動，估計結果將產生偏誤。因此，當面臨波灣戰爭之重大事件時，考量具間斷特性的跳躍模型有其必要性，藉以正確估計波動性。本文依據Chan (2003)所提出之雙變量跳躍GARCH模型估計原油與汽油間之波動性與相關性，並進一步探討兩次波灣戰爭期間，在價格上所造成之衝擊。實證結果發現，原油與汽油之跳躍點幾乎相同，但波動共移性的程度卻逐漸下降，共變異數在第二次波灣戰爭時明顯低於第一次波灣戰爭；而在波灣戰爭期間，原油之波動性高且較為敏感。再者，因戰爭所引起之大幅度波動皆未持續很長一段時間，符合跳躍模型之特性，因此，以此模型來估計原油商品的波動性是較為恰當的。
第三個主題探討樣本內估計期間長短對樣本外預測正確性所產生之影響，截至目前為止，少有文章將重心放在此研究主題上。本文同時採用預測包含力檢定(forecast encompassing)與預測誤差檢驗(mean square forecast errors, MSE)為模型選取的準則。一般而言，在適切的模型下，估計樣本期間越長，資訊漸趨完整，估計與預測結果將越正確；過短的估計期間將產生估計與預測偏誤的結果。針對此主題，本文針對一有結構性轉變之時間序列資料建立兩個實證模型，一包含結構性轉變，代表模型設定正確；另一則無結構性轉變，代表模型設定錯誤。此外，本文採用移動視窗與遞迴(recursive)的預測方式進行估計與預測，以檢驗樣本內估計期間長短對預測結果之影響。實證結果發現，正確模型的預測誤差隨著估計期間的增加而較低。當樣本估計期間較短時，將導致接受錯誤決策的結果。最後，本文將此結論應用於避險績效上，亦有一致性的結果，即避險績效在遞迴預測方式下最佳。

Risk measuring and forecasting are important issues in finance, however most literature focuses on the financial assets, and fewer papers discuss energy assets. The Petroleum market is characterized as highly volatile, the imbalance of supply and demand, the strategies adopted by the Organization of Petroleum Exporting Countries (OPEC), the interference of politics and so on have all stimulated prices. The oil prices have climbed up steadily recently, and it has not only shocked the petroleum market traders, but also influenced the financial market as well, owing to the high volatility of the crude oil. Thus the investigation of the crude oil risk is an important issue. This thesis analyzes the value-at-risk, the jump volatilities, and the forecast problems in crude oil of West Texas Intermediate (WTI), which modifies the shortcomings of traditional models in measurements and forecasts.
The first topic is discussing the Value-at-Risk (VaR). VaR is the most popular and attractive method of risk measuring. We estimate the VaR of the return on crude oil via RiskMetrics and the AR-GARCH model using the rolling bootstrapping methods. We adopt the bootstrapping method rather than using the Monte Carlo simulation or the historical simulation method because traditionally they are methods to estimate VaR. Even though they are traditional methods but they actually have the two severe problems of distribution assumption, Monte Carlo simulation, and a short observation period, historical simulation. The empirical results demonstrate that the bootstrapping method outperforms the no-bootstrapping method in the one-day-ahead VaR forecast but not in the ten-days-ahead forecasts. Furthermore, the performances of VaR forecasts are statistically indifferent in both the RiskMetrics and the AR-GARCH models.
The second topic is estimating the volatility of crude oil and gasoline while considering jumps. Previous studies in the literature almost all assumed that time series data follows a smooth and continuous volatility process. However, the presence of abnormal events induce serious violate in price, and the diffusion models are misspecified statistically. Therefore, considering the jump model with discrete characteristics is necessary while facing the abnormal events like two Gulf Wars. We further employ a correlated bivariate Poisson GARCH model suggested by Chan (2003) to investigate the relationship between the volatility of crude oil and gasoline; especially during the period of the Gulf War. We find that greater jumps occurring in crude oil returns will appear in gasoline returns at the same time, but the magnitude of the co-movements in volatility falls. The covariance is relatively smaller in the Second Gulf War compared to the first conflict. The volatility of crude oil is more sensitive than gasoline during the periods of wars. Furthermore, the jump that occurred by the war did not lead both spot prices to a high persistent level for a long period, which fits the feature of the jump models. 
The third topic investigates an essential problem of how to determine the estimation period in forecasting. Until now, less attention has been given to the problem of determining the appropriate estimation periods. Using the forecast encompassing and accuracy test, this investigation discusses the importance of considering the overall useful information in the in-sample period. An excessively short sample period will increase the variance of the parameter estimation and bias the out-of-sample forecasts. This study further constructs a nested linear regression model, either with or without the structural change, depending on the existence of a break, and comparing the performance of the two versions of the model for each estimation period and forecast scheme. The empirical results demonstrate that forecasts under the correct model reduces both measurement loss and the mean square forecast as we increase the in-sample estimation period. For the forecast accuracy and encompassing tests, the use of fewer observations in making an estimate could easily lead to wrong decisions and the acceptance of the wrong model. Finally, these results are also consistent with the hedge effectiveness, namely that the effectiveness is better under the recursive scheme in terms of considering all useful information.

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENT												i
ABSTRACT IN CHINESE												ii
ABSTRACT IN ENGLISH												iv
LIST OF TABLES														xi
LIST OF FIGURES													xii

PART I
Modeling Value-at-Risk for Oil Prices Using a Bootstrapping Approach
ABSTRACT															2
CHAPTER
1. Introduction													3
1.1 Motivations and Objectives										3
1.2 Flow Chart													5
2. Literature Review												6
2.1 Value-at-Risk in Crude Oil										6
2.2 Calculating the VaR											6
2.3 Observation Periods and Out-of-Sample Forecast					9
3. Measurement of Value-at-Risk									11
3.1 Definition of VaR												11
3.2 Statistical Tests												11
3.3 Estimate Methodology: Bootstrapping								12
3.4 Empirical Models												13
3.5 Observation Periods and Out-of-Sample Forecast in Rolling Window	15
4. Empirical Results												16
4.1 Data														16
4.2 Estimated Results of the RiskMetrics Method: Mean of the Decay Factor
																16
4.3 Estimated Results and the Adaptation of the AR(1)-GARCH(1,1) Method
																17
4.4 Failure Rates and the Performance of VaR Models					19
5. Conclusions													23
Bibliography															24

PART II
Correlated Jumps in Crude Oil and Gasoline during the Gulf War
ABSTRACT															28
CHAPTER
1. Introduction													29
1.1 Motivations and Objectives										29
1.2 Flow Chart													32
2. Literature Review												33
2.1 The Jump Model												33
2.2 The Bivariate Jump Model										34
3. Correlated Bivariate Poisson GARCH Model (CBP-GARCH)			36
3.1 Definition													36
3.2 The Probability Function of Jump and the Jump Intensity				37
3.3 GARCH Function												38
4. Empirical Results												40
4.1 Data														40
4.2 The Empirical Results of the CBP-GARCH Model					41
4.3 The Effects of Wars and Politics									45
4.4 The Covariance between Crude Oil and Gasoline					48
5. Conclusions													50
Bibliography															51

PART III
Enhancing the Forecast Accuracy by Using Long Estimation Periods
ABSTRACT															55
CHAPTER
1. Introduction													56
1.1 Motivations and Objectives										56
1.2 Flow Chart													58
2. Literature Review												59
2.1 Sample Period Length											59
2.2 Rolling Scheme vs. Recursive Scheme								59
2.3 Constructing Model with Structural Break							60
2.4 Out-of-Sample Forecast Error Tests								61
3. Methodology													63
3.1 The Model-Setting and Forecast Scheme							63
3.2 Forecast Accuracy and Forecast Encompassing Tests					63
4. Empirical Results												65
4.1 Data and the Empirical Model									65
4.2 The Empirical Results											66
4.2.1 Under the Rolling Scheme									66
4.2.2 Under the Recursive Scheme								68
4.3 Application in Hedge Effectiveness								69
5. Conclusions													72
Bibliography       73											
LIST OF TABLE Page
PART I
Table 1. The mean of λ with the RiskMetrics method							16
Table 2. RESET test													17
Table 3. The empirical results of the AR(1)-GARCH(1,1) model					18
Table 4. The number of failure and the failure rates							20
Table 5. Failure rate test													21

PART II
Table 1. Descriptive statistics												40
Table 2. Empirical results of CBP model									42
Table 3. The covariance of crude oil and gasoline price in different periods			49

PART III
Table 1. Empirical results under the rolling scheme							67
Table 2. Empirical results under the recursive scheme							69
Table 3. Hedge effectiveness												71

 
LIST OF FIGURES
Page
PART I
Figure 1. The time series plot of crude oil prices from 1994/1/1 to 2004/7/31		3
Figure 2. The definition of observation periods and holding period				15
Figure 3. Crude oil returns and VaR with one-day-ahead forecast and 500-days
observation periods												21
Figure 4. Crude oil returns and VaR with ten-days-ahead forecast and 500-days
observation periods												22

PART II
Figure 1. The time series plot of the spot price of crude oil and gasoline			30
Figure 2. Returns of crude oil and gasoline									41
Figure 3. Time varying jump intensities in crude oil and gasoline					44
Figure 4. Correlated jump intensities and jump counter correlations				44
Figure 5. Jump variance in crude oil and gasoline								45
Figure 6. Jump covariance in crude oil and gasoline							45
Figure 7. The jump conditional variances and covariance during Gulf War I		48
Figure 8. The jump conditional variances and covariance during Gulf War II		48

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