臺灣博碩士論文加值系統

近年來金融環境變化迅速，由於新金融商品的開放及金融機構間激烈的競爭，金融機構無不增加其交易活動以改善其獲利，隨之也帶來顯著的市場風險。市場風險值（Value-at-Risk，VaR）目前已經成為衡量金融機構市場風險的標準方法。
本研究導入一不對稱GARCH模型－GJR-GARCH模型，來計算市場風險值，探討使用GJR-GARCH模型是否可以更精確地衡量金融機構的市場風險。由於缺乏實際的每日交易損益資料，我們模擬兩個投資組合A和B，分別代表富邦和國泰世華金融控股公司。模擬資料持有期間從2000年11月28日 至 2003年4月15日，其中400筆資料點當作樣本用來估計參數，而剩下的資料點則用來比較模型估計出之市場風險值，看其預測能力如何。
我們發現使用GJR-GARCH模型可有效預測市場風險值，然而用作比較之對稱GARCHM模型也同樣具有良好的預測能力，和先前研究相比，似乎並沒有存在槓桿效果。我們更進一步每隔五日更新所估計之參數，在不同的模型比較下，我們發現更新參數可使模型衡量更為精確。但是不可諱言的，每日交易損益超出市場風險值的次數和資本計提負擔之間必須互相取捨，不可兼得。

Financial environment has changed more rapidly in recent years. Due to the opening of innovative financial products and vigorous competition, the trading activities are increasing and produce significant market risk. Value-at-Risk（VaR）now has become a standard measure of financial market risk.
In this study, we introduce an asymmetric GARCH model, GJR-GARCH, in Value-at-Risk. We want to see if GJR-GARCH is a better method to evaluate the market risk of financial holdings. Because of lacking the actual daily P＆L data, we simulated portfolio A and B, representing FuBon and Cathay financial holdings. The holding period stretches from 2000/11/28 to 2003/4/15. We take 400 observations as Sample Group to do the backward test and use the rest observations to forecast the change of VaR
We find GJR-GARCH works very well in VaR forecasting. However, it also performs very well under the symmetric GARCHM model. There seems no leverage effect as the previous study. Further, we open a 5-day moving window to update parameter estimates. Comparing the results under different models, we find that the model is more accurate by updating parameter estimates. It is a trade-off between violations and capital charges

Contents
Chapter 1 Introduction...........................................................................................1
1.1 Motivations and Purposes ................................................................................1
1.2 Framework .......................................................................................................4
Chapter 2 Basle Ⅱ and Market Risk ..................................................................6
2.1 Basle Ⅱ...........................................................................................................6
2.2 Market Risk Amendment .................................................................................8
2.3 Trading Book Issues in Basle Ⅱ.....................................................................9
Chapter 3 Literature Review ...............................................................................11
Chapter 4 Data ......................................................................................................14
4.1 Assumptions by Wang（2003）....................................................................15
4.2 Portfolio Formation........................................................................................16
4.3 Holding Period and Daily P&L......................................................................17
Chapter 5 Methodology........................................................................................19
5.1 GJR-GARCHM (1,1).....................................................................................20
5.2 GARCHM (1,1) .............................................................................................21
Chapter 6 Empirical Results................................................................................23
6.1 Backward Test................................................................................................23
6.2 Value-at-Risk in GJR-GARCHM...................................................................25
6.3 Value-at-Risk under GARCHM.....................................................................27
6.4 Model Comparison.........................................................................................27
Chapter 7 Conclusion ...........................................................................................28
References...................................................................................................................30

Figures
Figure 1...................................................................................................................32
Structure of Basle Ⅱ
Figure 2...................................................................................................................33
Distribution of Daily P&L of Portfolio A（2000/11/28－2003/4/15）
Figure 3...................................................................................................................33
Distribution of Daily P&L of Portfolio A（2000/11/28－2003/4/15）
Figure 4...................................................................................................................34
P＆L Returns and VaR of Portfolio A under ARMA(1,1)-GJR GARCHM(1,1)
Figure 5...................................................................................................................35
P＆ L Returns and VaR of Portfolio B under ARMA(1,1)-GJR GARCHM(1,1)
Figure 6...................................................................................................................36
P＆L Returns and VaR of Portfolio A under AR(1)-GJR GARCHM(1,1)
Figure 7...................................................................................................................37
P＆L Returns and VaR of Portfolio B under AR(1)-GJR GARCHM(1,1)
Figure 8...................................................................................................................38
P＆L Returns and VaR of Portfolio A under MA(1)-GJR GARCHM(1,1)
Figure 9...................................................................................................................39
P＆L Returns and VaR of Portfolio B under MA(1)-GJR GARCHM(1,1)
Figure 10..................................................................................................................40
P＆L Returns and VaR of Portfolio A under Different Modles in ARMA(1,1) at 99% confidence level
Figure 11..................................................................................................................41
P＆L Returns and VaR of Portfolio A under Different Modles in ARMA(1,1) at 95% confidence level
Figure 12..................................................................................................................42
P＆L Returns and VaR of Portfolio B under Different Modles in ARMA(1,1) at 99% confidence level
Figure 13..................................................................................................................43
P＆L Returns and VaR of Portfolio B under Different Modles in ARMA(1,1) at 95% confidence level
Figure 14..................................................................................................................44
P＆L Returns and VaR of Portfolio A under Different Modles in AR(1) at 99% confidence level
Figure 15..................................................................................................................45
P＆L Returns and VaR of Portfolio A under Different Modles in AR(1) at 95% confidence level
Figure 16..................................................................................................................46
P＆L Returns and VaR of Portfolio B under Different Modles in AR(1) at 99% confidence level
Figure 17..................................................................................................................47
P＆L Returns and VaR of Portfolio B under Different Modles in AR(1) at 95% confidence level
Figure 18..................................................................................................................48
P＆L Returns and VaR of Portfolio A under Different Modles in MA(1) at 99% confidence level
Figure 19..................................................................................................................49
P＆L Returns and VaR of Portfolio A under Different Modles in MA(1) at 95% confidence level
Figure 20..................................................................................................................50
P＆L Returns and VaR of Portfolio B under Different Modles in MA(1) at 99% confidence level
Figure 21..................................................................................................................51
P＆L Returns and VaR of Portfolio B under Different Modles in MA(1) at 95% confidence level

Tables
Table 1...................................................................................................................52
Summary for Operational Income and Net Profit and Loss（P&L）for Subsidiaries in Fu Bon Financial Holding Company
Table 2...................................................................................................................52
Summary for Operational Income and Net Profit and Loss（P&L）for Subsidiaries in Cathay Financial Holding Company
Table 3...................................................................................................................53
Size and Allocation of Portfolio A Categorized by Investment Asset Classes
Table 4...................................................................................................................53
Size and Allocation of Portfolio B Categorized by Investment Asset Classes
Table 5...................................................................................................................53
Percentage of Investment Asset Allocation for Portfolio A and B
Table 6...................................................................................................................54
Details of Positions and Investing Instruments for Portfolio A
Table 7...................................................................................................................57
Details of Positions and Investing Instruments for Portfolio B
Table 8...................................................................................................................59
P&L Returns Statistics Summary for Portfolio A and B （2000/11/28－2003/4/15）
Table 9...................................................................................................................59
P&L Returns Statistics Summary for Sample Groups（2000/11/28－2003/3/1）
Table 10..................................................................................................................60
Likelihood Ratio Test for Portfolio A and B
Table 11..................................................................................................................61
Summery of Parameters for under GJR-GARCHM
Table 12..................................................................................................................62
Summery of Parameters under GARCHM
Table 13..................................................................................................................63
VaR Comparison under mean equation of ARMA(1,1)
Table 14..................................................................................................................64
VaR Comparison under mean equation of AR(1)
Table 15..................................................................................................................65
VaR Comparison under mean equation of MA(1)

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