||The Empirical Research of Measurement on Liquidity Risk, Operational Risk and Sovereign Risk
||Department of Banking and Finance
Value at risk
Interest rate parity
Copula- ARMAX-GJR-GARCH model
第一部分、流動性風險的衡量實證研究係以蒐集台灣全體金融機構於2002年9月16日至2010年8月31日期間，參加大額支付系統的金融機構支付中央銀行之日間透支利息之成本資料，進行實證建模及估計銀行流動性成本風險尾部參數。本研究首先考量巴賽爾資本協定III有關改進衡量標準之概括性設計，是否有助於提升銀行部門吸收財務及經濟壓力帶來衝擊之能力，並藉以瞭解支付系統之流動性風險的特性與集中度，再者運用配適一般化柏瑞圖分配(Generalized Pareto Distribution, GPD)並透過標準參數模型比較，以拔靴法(Bootstrap)估計該參數之信賴區間。另計算風險值(Value at Risk, VaR)及期望損失(Expected Shortfall, ES)以有效衡量流動性風險。研究結果顯示在大額支付系統下銀行之流動性損失的尾部行為，能提供精準及有用資訊予金融監理主管機關及中央銀行當局參考。本研究亦成功地應用統計方法，藉由潛在監理行動衡量分析台灣銀行體系之流動性成本，以有效建立另一種監理方法。
||This dissertation includes three aspects of the empirical study of measurement on liquidity risk, operational risk and sovereign risk illustrate as follows:
First, using the intraday overdraft cost of all Taiwanese banks pay to Central Bank (CB) in the Large Value Payment System (LVPS) to measure the liquidity risk from Sep 16, 2002 to Aug 31, 2010, I collected the interest cost of overdraft to focus on modeling and estimating tail parameters of bank liquidity cost. I first take into account to illustrate whether the Basel III is a comprehensive set of reform measures, to improve the banking sector’s ability to absorb shocks arising from financial and economic stress and to understand the characteristic and concentration of liquidity risk of payment system. I further centralize the Generalized Pareto Distribution (GPD) and compare it with standard parametric modeling. Bootstrap method is used to estimate the confidence interval of parameters. In addition, Value at Risk (VaR) and expected shortfall (ES) calculations were performed. My results captured the tail behavior of banks’ liquidity losses from the LVPS, which provide the precise and useful information for the supervisory authorities and the central bank of Taiwan. I contributed to setting alternative oversight method by using potential supervisory action to measure liquidity cost of the banking system of Taiwan, and apply the statistic methodology successfully.
Secondly, from the loss data associated with significant operational risks of Taiwanese commercial banks over the period from 1995 to 2009, I collected a set of 323 observations to use for modeling and estimating tail parameters of bank’s operational distribution. By means of three copula functions, I calculated correlations between event pairs, test for independent between different classifications of risk types of the Basel II framework and seek to understand the characteristic and concentration of commercial banks’ operational risks. Further, I estimated parameters for the generalized Pareto distribution (GPD) and compare its fit with those of standard parametric models. A bootstrap method is used to estimate the confidence intervals for parameter values. In addition, value-at-risk (VaR) and expected shortfall (ES) calculations are performed. My result provides important information that financial supervisory authorities can use when accounting for operational losses of commercial banks. This research also contributes to the measurement of Taiwanese commercial banks operational risk capital for the banks.
Last, I provided new evidence regarding the shock effects of the PBC intervention in the FX market by comparing the volatility of exchange rate of Euro dollar (EUD) and Chinese Ranminbi (RMB) against the US dollar (USD) and showing policy interference of Chinese the exchange rate system. Firstly I modeled the ARMAX-GJR-GARCH equation to reexamine interest parity theory and find the structure break of the exchange rate of the RMB then I set up the new Copula-ARMAX-GJR-GARCH model by using daily exchange rate of EUD and RMB against USD during the period from January 2005 to March 2010. The result provides the very important information that I proved the sovereign risk of official intervention and political influence economy. My new research also contributes to examine a discrepancy between the exchange rate system of EU and China for risk managers in financial institutions.
List of Tables vi
List of Figures vii
Chapter 1 Introduction 1
1.1 Motivations 2
1.2 Objectives 2
1.3 The structure of this dissertation 3
1.4 The measurement of liquidity risk for Taiwanese banks from the LVPS 4
1.5 The measurement of capital for operational risk in Taiwanese commercial banks 7
1.6 The measurement for sovereign risk of official intervention by the volatility relationship between EUD and RMB 9
Chapter 2 Methodology, theory and models 12
2.1 The measurement methodology of liquidity risk and operational risk 13
2.1.1 Extreme value theory 13
2.1.2 Generalized Pareto distribution 13
2.1.3 Steps in applying GPD to exploratory data analysis 14
2.1.4 Threshold selection 14
2.1.5 Calculation of VaR 15
2.1.6 Expected shortfall 16
2.1.7 Goodness-of-fit 17
2.2 Copula function-a brief review 18
2.3 The theory model for sovereign risk of official intervention 20
2.3.1 Applying the interest rate parity 20
2.3.2 Theoretical models 21
2.3.3 Copula-ARMAX-GJR-GARCH model 21
Chapter 3 Empirical results and analysis 25
3.1 The empirical results for measurement of liquidity risk 26
3.1.1 Data description 26
3.1.2 Empirical results analysis 26
3.2 The empirical results for measurement of operational risk 33
3.2.1 Data description 33
3.2.2 Empirical results analysis 33
3.3 The empirical results in sovereign risk of official intervention 50
3.3.1 Data description 50
3.3.2 Empirical results analysis 50
Chapter 4 Conclusion 57
4.1 The conclusion for measurement of liquidity risk 58
4.2 The conclusion for measurement of operational risk 60
4.3 The conclusion for sovereign risk of official intervention by the volatility
relationship between EUD and RMB 62
List of Tables
Table 1 Frequencies of liquidity loss data 27
Table 2 Summary statistics for liquidity loss data 27
Table 3 Parametric estimations for fitted functions 28
Table 4 The VaR and ES of GPD 31
Table 5 Goodness-of-fit for GPD model 32
Table 6 Bootstrap confidence intervals for GPD 32
Table 7 Basel II operational risk factors & event type classification 34
Table 8 Statistics for operational risk event types 34
Table 9 Results of copula Kendall tau for event-pairs 36
Table 10 Test of independent for event-pairs 40
Table 11 Summary statistics 41
Table 12 Parametric estimations for fitted functions 42
Table 13 The VaR and ES of GPD 47
Table 14 Goodness-of-fit for GPD model 48
Table 15 Bootstrap confidence intervals for GPD 48
Table 16 The results of Chow test 51
Table 17 Results from the ARMAX–GJR-GARCH(1,1)model-EUD 52
Table 18 Results from the ARMAX–GJR-GARCH(1,1)model-RMB 53
Table 19 The Kendall’s tau of copula functions-innovations between EUD and RMB 56
Table 20 The Kendall’s tau of copula functions-between EUD and RMB exchange rate 56
List of Figures
Figure 1(a). 1-F(x) on logarithmic scaling in X-axis 27
Figure 1(b). 1-F(x) for empirical distribution of a sample27
Figure 1(c). P-P plot for liquidity loss data 27
Figure 1(d). Q-Q plot for liquidity loss data 27
Figure 2(a). The lognormalpdfplot of liquidity loss amount29
Figure 2(b). The exponential pdf plot of liquidity loss amount 29
Figure 2(c). The Gamma pdf plot of liquidity loss amount 29
Figure 2(d). The GPD pdf plot of liquidity loss amount 29
Figure 3. The mean excess function (MEF) of liquidity loss amount 30
Figure 4. Hill plot, the mean excess function of liquidity loss amount 30
Figure 5. The bootstrap estimate of parameter (threshold=13,050) 32
Figure 6(a). The scatter plot of original data and copula for E1-E2 37
Figure 6(b). The scatter plot of original data and copula for E1-E6 37
Figure 6(c). The scatter plot of original data and copula for E1-E7 38
Figure 6(d). The scatter plot of original data and copula for E2-E6 38
Figure 6(e). The scatter plot of original data and copula for E2-E7 39
Figure 6(f). The scatter plot of original data and copula for E6-E7 39
Figure 7. The box plots of event-pairs 40
Figure 8. The empirical distribution of operational losses41
Figure 9(a). The exponential pdf plot of loss amount 43
Figure 9(b). The gamma pdf plot of loss amount 43
Figure 9(c). The weibull pdf plot of loss amount 43
Figure 9(d). The GPD pdf plot of loss amount 43
Figure 10(a). The exponential CDF plot of loss amount 44
Figure 10(b). The gamma CDF plot of loss amount 44
Figure 10(c). The weibull CDF plot of loss amount 44
Figure 10(d). The GPD CDF plot of loss amount 45
Figure 11. The mean excess function of loss amount 46
Figure 12. The hill plot of loss amount 46
Figure 13. The QQ-plot and PP-plot of loss amount to exponential distribution 46
Figure 14. Box plot to identify outliers for all loss amounts 47
Figure 15. Histogram of bootstrap for parameter ξ and σ at different thresholds 49
Figure 16. The return of EUD and RMB exchange rate 51
Figure 17. Time varying normal copula Kendall’s tau EUD and RMB exchange rate 54
Figure 18. The dynamic dependence of panel A, panel B and panel C 54
Figure 19. The scatter plot of two series 55
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