臺灣博碩士論文加值系統

The asymptotic single risk factor approach (ASRF) approach is a simplified framework for determining regulatory capital charges for credit risk and has become an integral part of how credit risk capital requirements are to be determined under the Basel II. Within this approach, a key regulatory parameter is the average asset return correlation. In this paper, I examine the empirical relationship between the asset return correlation, firm probability of default and firm asset size in five models. According to previously theoretical background, I separate these models into two parts. First part I called Market Correlation Model, which conclude Basel and KMV’s factor Model, and the results in these models advocate the explanation for a higher asset return correlation of large firms may be that they are better diversified than small firms. Second part I called Asst Value Correlation Model, which conclude one factor model; default correlation model and structure model, and the results in these models advocate the issue of “financial accelerator” which means macroeconomics shocks should have a stronger impact on small firms and we should observe a higher asset return correlation. Especially in structure model which I devised, it not only concludes the advantage of Market Correlation Model but also combines the default point in Asset value correlation model. Furthermore, I prove the one factor model and default correlation model under some conditions are the same. In our empirical results, we can find that the range of asset return correlation in Basel Model is the largest range number than others and I also find the volatility of probability default has a strong impact on asset return correlation.

INDEX
1. Introduction…………………………………………………….……...…………1
2. Review ofrelevant literature…………………………………………..………….5
2.1 Regulatory Capital and the Basel Initiative……………………..…………..5
2.2 An Overview of Today’s Industry Models………………………………… 7
2.3 Review of the Literature---Asset Return Correlation Coefficient………….9
2.4 Further Discussions─Asset Return Correlation Coefficient………..…….14
3. Empirical Methodology………………...…………………..……………………17
3.1 Market Correlation Model ………………………………………..………...17
3.1.1Overview of the framework proposed by the Basel Committee….……...15
3.1.2KMV’s Factor Model………………..………………….…………………..29
3.2 Asset Value Correlation Model…………………………….………………..22
3.2.1 The one-factor model (Gordy, 2000)…………..……………….…………22
3.2.2 Default Correlation Model…………………..………………..…………...26
3.2.3 Structure Model …………………………………………….……………..28
4. Data Description………………………..……………………..…..……………. 32
5. Empirical Results and A Comprehensive Discussion …………………………34
5.1 The Empirical Result in Market Correlation Model……………………..34
5.1.1 The relationship between PD and firm size in Market
Correlation Model………………………………………………………34
5.1.2 The relationship between asset return correlation and firm size
in Market Correlation Model……………………………………………34
5.1.3 The relationship between PD and asset return correlation in
Market Correlation Model………………………………………………34
5.2 The Empirical Result in Asset Value Correlation Model…………………..35
5.2.1 The relationship between PD and firm size in Asset
value Model……………………………………………………………….35
5.2.2 The relationship between asset return correlation and firm size in
Asset value Model………………………………………………………...35
5.2.3 The relationship between PD and asset return correlation in Asset
Value Model………………………………………………………………35
5.3 Further Discussion about the Relationship PD, firm size and asset
return correlation……………………………………………………………..36
5.4 Comparison for Five models based on Probability default Categories and Firm Size Categories……………………………………………………………40
5.5 The Range of Asset Return Correlation in Five Models ……………………41
5.6 Compare One Factor model with Default Correlation Model.......................42
6. Conclusion………………………………………………………………………...45
Reference………………………………………………………………..………47
Appendix A………………………………………………………………………51
Appendix B……………………………………………………………………....62
Appendix C…………………………………………………………………..….65
INDEX (TABLES)
Table2.1 Overview: Main Difference between Industry Models ………………….9
Table 4.1 Historical default probability data (1981-1997) by rating class ……...33
Table 5.1 the correlation between firm size and PD in five Models……………...37
Table 5.2 the correlation between firm size and asset return correlation in
five Models………………………………………………………………38
Table5.3 the correlation between firm size and asset return correlation in
five Models………………………………………………………………..38
Table5.4 The Spearman’s correlation Test Results……………………………….39
Table 5.5 Comparison of Asset Return Correlation for the Five models based
on PD categories and firm size categories…………………………….40
Table5.5 the Range of Asset Return Correlation in Five Models………………..41
Table5.6 Volatility of probability default in five models…………………………42
Table 5.A Descriptive statistic of PD, Asset return correlation and Firm size
in Basel Commitment model…………………………………………...51
Table5.B Descriptive statistic of PD, Asset return correlation and Firm size
in KMV’s Factor model…………………………………………………51
Table5.C Descriptive statistic of PD, Asset return correlation and Firm size
in one factor model……………………………………...………………52
Table5.D Descriptive statistic of PD, Asset return correlation and Firm size
in default correlation model …………………………………………...52
Table5.E Descriptive statistic of PD, Asset return correlation and Firm size
in structure model………………………………………………………53
Table 6.A Descriptive the value of asset return correlation based on
rating category in the Basel Commitment Model…………………….53
Table6.B Descriptive the value of asset return correlation based on
rating categories in the KMV’s factor Model…………………………54
Table 6.C Descriptive the value of asset return correlation based on
rating categories in One Factor Model…………………………….…..54
Table 6.D Descriptive the value of asset return correlation based on rating categories in Default Correlation Model………………………………55
Table 6.E Descriptive the value of asset return correlation based on
rating categories in the Structure Model ……………………………...55
Table B Empirical default frequency and volatility …………………………..….64
INDEX (Figures)
Figure2.1 Today’s Best-Practice Industry Models………………………………... 8
Figure3.1 Three- level factor structure in KMV’s Global Correlation ModelTM ,see also comparable presentation in the literature………...22
Figure 5.1 Relationship between PD and its volatility in five models……………41
Figure 7.A Relationship between PD and Firm size in Basel Commitment
；KMV’s Factor ; One Factor ; Default Correlation model …………56
Figure7.B Relationship between PD and Firm size in the Structure model……..56
Figure 8.A Relationship between Asset return correlation and Firm size in
Basel Commitment model …………………………………………….56
Figure 8.B Relationship between Asset return correlation and Firm size in KMV’s Factor model …………………………………………………57
Figure8.C Relationship between Asset return correlation and Firm size in
One Factor Model ………………………………………………………57
Figure8.D Relationship between Asset return correlation and Firm size in
default correlation model………………………………………………57
Figure 8.E Relationship between Asset return correlation and Firm size
in Structure model………………………………………………………58
Figure 9.A Relationship between Asset return correlation and PD in
Basel Commitment model…………………………………………….58
Figure 9.B Relationship between Asset return correlation and PD in
KMV’s Factor model …………………………………………………58
Figure 9.C Relationship between Asset return correlation and PD in One
Factor Model…………………………………………………………..59
Figure 9.D Relationship between Asset return correlation and PD in
Default Correlation Model……………………………………………59
Figure 9.E Relationship between Asset return correlation and PD in
the Structure model……………………………………………………59
Figure10.A. Calibrated Asset Return Correlation for Basel Committee
Model based on PD Categories and Firm Size Categories………...60
Figure10.B. Calibrated Asset Return Correlation for KMV’s factor Model
based on PD Categories and Firm Size Categories………………...60
Figure10.C. Calibrated Asset Return Correlation for one-factor Model
based on PD Categories and Firm Size Categories……………...…61
Figure10.D. Calibrated Asset Return Correlation for Default Correlation
Model based on PD Categories and Firm Size Categories………...61
Figure10.E. Calibrated Asset Return Correlation for structure Model
based on PD Categories and Firm Size Categories………………..62

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