1 1.1 Merton (1974) Black and Cox (1976) PD Probability of Default LGD Loss Given Default 1 EAD Exposure At Default II Merton (1974) Merton Merton Ges

Size: px

Start display at page:

Download "1 1.1 Merton (1974) Black and Cox (1976) PD Probability of Default LGD Loss Given Default 1 EAD Exposure At Default II Merton (1974) Merton Merton Ges"

たしろうさわい
5 years ago
Views:

1 II 2 :,,,,. CRD ed061001@srv.cc.hit-u.ac.jp yamasita@ism.ac.jp 1

2 1 1.1 Merton (1974) Black and Cox (1976) PD Probability of Default LGD Loss Given Default 1 EAD Exposure At Default II Merton (1974) Merton Merton Geske (1977) Guha and Sbuelz (2002) Guha and Sbuelz (2004) (2007) Merton Black and Cox (1976) Longstaff and Schwartz (1995) Giesecke (2006) First Passage Time Model Zhou (2001) (2007) Jarrow and Turnbull (1995) Madan and Unal (1998) Duffie and Singleton (1999) 1 =1 LGD 2

3 2 Jarrow (2001) (2004) 3 II Asarnow and Edwards (1995) Hurt and Felsovalyi (1998) Asarnow and Edwards (1995) Araten, Jacobs and Varshney (2004) JP 2 3 Frye (2000) (2005) 4 Basel Committee on Banking Supervision (2006) 3

4 Franks, de Servigny and Davydenko (2004) 10 GDP Dermine and de Carvalho (2006) Banco Comercial Português log-log GLM Franks et al. (2004) GDP Asarnow and Edwards (1995) USA yes Hurt and Felsovalyi (1998) LA yes Araten et al. (2004) USA yes Franks et al. (2004) UK yes Franks et al. (2004) FRA yes Franks et al. (2004) GER yes Dermine and Carvalho (2006) POR yes 1: 5 5 Grunert and Weber (2007) table 1 LA POR 6 Araten et al. (2004) Franks et al. (2004) GDP Araten et al. (2004) Moody s All-Corporate 4

5 Franks et al. (2004) Franks et al. (2004) Dermine and Carvalho (2006) Araten et al. (2004) Dermine and Carvalho (2006) Asarnow and Edwards (1995) Hurt and Felsovalyi (1998) Franks et al. (2004) Dermine and Carvalho (2006) GDP Dermine and Carvalho (2006) Franks et al. (2004) Araten et al. (2004) Dermine and Carvalho (2006) Franks et al. (2004) Araten et al. (2004) Franks et al. (2004) 2 2: (2005) % 90% % 5

6 単位 : 兆円保証承諾額保証債務残高代位弁済額回収金額年度 1: HP / 6

7 60% 50% 40% 30% 代位弁済率回収率 20% 10% 0% 年度 2:

8 A B C A B C % 9.49% 8.06% % 81.43% 61.40% ( ) 4,246,182,062 34,208,543,975 7,608,757,883 ( ) 1,048,186,027 8,986,802,033 1,268,310, % 26.27% 16.67% 3: Hurt and Felsovalyi (1998) Dermine and Carvalho (2006) Asarnow and Edwards (1995) Franks et al. (2004)

9 A B C 16.53% 7.97% 12.69% 32.14% 19.76% 27.58% % 20.98% 64.45% 44.66% 29.14% 44.74% % 8.13% 23.65% 43.14% 19.82% 38.32% % 7.25% 13.63% 32.39% 18.12% 27.13% % 64.79% 45.42% 38.87% 38.25% 39.02% % 9.94% 24.84% 37.88% 22.94% 35.26% % 3.35% 9.21% 30.99% 9.19% 22.80% % 18.44% 33.81% 43.52% 32.15% 41.97% % 6.53% 18.74% 39.54% 17.88% 33.80% : 13 A B C p : 14 9

10 回収率千万 1 億 2 億代位弁済額 ( 単位 : 円 ) 担保付き通常担保付き金融安定化特別保証担保なし通常担保なし金融安定化特別保証 3: A 24 回収率千万 1 億 2 億代位弁済額 ( 単位 : 円 ) 担保付き通常担保付き金融安定化特別保証担保なし通常担保なし金融安定化特別保証 4: B 24 10

11 回収率千万 1 億 2 億代位弁済額 ( 単位 : 円 ) 担保付き通常担保付き金融安定化特別保証担保なし通常担保なし金融安定化特別保証 5: C A p % 11

12 3 24 回収率 200% 180% 160% 140% 120% 100% 80% 60% 40% 20% 0% 1 ヶ月 2 ヶ月 3 ヶ月 4 ヶ月 5 ヶ月 6 ヶ月 7 ヶ月 8 ヶ月 9 ヶ月 10 ヶ月 11 ヶ月 12 ヶ月 13 ヶ月 14 ヶ月 15 ヶ月 16 ヶ月 17 ヶ月 18 ヶ月 19 ヶ月 20 ヶ月 21 ヶ月 22 ヶ月 23 ヶ月 24 ヶ月代位弁済後経過時間 6: A i t X i,t X i,t = 0 X i,t 0 i t MRR i,t MRR i,t = X i,t B i B i i 9 10 C

13 回収率 140% 120% 100% 80% 60% 40% 20% 0% 1 ヶ月 2 ヶ月 3 ヶ月 4 ヶ月 5 ヶ月 6 ヶ月 7 ヶ月 8 ヶ月 9 ヶ月 10 ヶ月 11 ヶ月 12 ヶ月 13 ヶ月 14 ヶ月 15 ヶ月 16 ヶ月 17 ヶ月 18 ヶ月 19 ヶ月 20 ヶ月 21 ヶ月 22 ヶ月 23 ヶ月 24 ヶ月代位弁済後経過時間 7: A 回収率 120% 100% 80% 60% 40% 20% 0% 1 ヶ月 2 ヶ月 3 ヶ月 4 ヶ月 5 ヶ月 6 ヶ月 7 ヶ月 8 ヶ月 9 ヶ月 10 ヶ月 11 ヶ月 12 ヶ月 13 ヶ月 14 ヶ月 15 ヶ月 16 ヶ月 17 ヶ月 18 ヶ月 19 ヶ月 20 ヶ月 21 ヶ月 22 ヶ月 23 ヶ月 24 ヶ月代位弁済後経過時間 8: A

14 相対頻度 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 9 ヶ月 5 ヶ月 17 ヶ月 13 ヶ月 21 ヶ月代位弁済後経過時間回収率 100% 110% 120% 130% 140% 150% 1 ヶ月 9: C 相対頻度 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150% 回収率代位弁済後経過時間 1ヶ月 2ヶ月 3ヶ月 4ヶ月 5ヶ月 6ヶ月 7ヶ月 8ヶ月 9ヶ月 10ヶ月 11ヶ月 12ヶ月 13ヶ月 14ヶ月 15ヶ月 16ヶ月 17ヶ月 18ヶ月 19ヶ月 20ヶ月 21ヶ月 22ヶ月 23ヶ月 24ヶ月 10: C 16 14

15 4.3 i B i > 0 T CRR i,t CRR i,t = T t=1 X i,t B i X i,t 0 CRR i,t 0 17 CRR i,t 1 0 CRR i,t B i e rt r > 0 T % 100% Hartigan and Hartigan (1985) dip 1% 24 A B C dip % A B C 15

相対頻度 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 回収率 100% 110% 120% 130% 140% 150% 22ヶ月 19ヶ月 16ヶ月 13ヶ月 10ヶ月代位弁済後 7ヶ月経過時間 4ヶ月 1 ヶ月 11: C 相対頻度 90% 80% 70% 60% 50% 40%

16 相対頻度 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 回収率 100% 110% 120% 130% 140% 150% 22ヶ月 19ヶ月 16ヶ月 13ヶ月 10ヶ月代位弁済後 7ヶ月経過時間 4ヶ月 1 ヶ月 11: C 相対頻度 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150% 回収率代位弁済後経過時間 1ヶ月 2ヶ月 3ヶ月 4ヶ月 5ヶ月 6ヶ月 7ヶ月 8ヶ月 9ヶ月 10ヶ月 11ヶ月 12ヶ月 13ヶ月 14ヶ月 15ヶ月 16ヶ月 17ヶ月 18ヶ月 19ヶ月 20ヶ月 21ヶ月 22ヶ月 23ヶ月 24ヶ月 12: C 19 16

17 相対頻度 45% 40% 35% 30% 25% 20% 保証協会 A 保証協会 B 保証協会 C 15% 10% 5% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150% 160% 170% 180% 190% 200% 回収率 13: A B C T P RER T P RER T = T N N T 1 14 T P RR T N T i=1 t=1 P RR T = X i,t N i=1 B i = N w i CRR i i=1 B i i w i = B i P N i=1 B i P RR T 15 17

18 ポートフォリオ回収実行率 90% 80% 70% 60% 50% 40% 保証協会 A 保証協会 B 保証協会 C 30% 20% 10% 0% 1 ヶ月 3 ヶ月 5 ヶ月 7 ヶ月 9 ヶ月 11 ヶ月 13 ヶ月 15 ヶ月 17 ヶ月 19 ヶ月 21 ヶ月 23 ヶ月代位弁済後経過時間 14: A B C ポートフォリオ累積回収率 30% 25% 20% 15% 保証協会 A 保証協会 B 保証協会 C 10% 5% 0% 1 ヶ月 3 ヶ月 5 ヶ月 7 ヶ月 9 ヶ月 11 ヶ月 13 ヶ月 15 ヶ月 17 ヶ月 19 ヶ月 21 ヶ月 23 ヶ月代位弁済後経過時間 15: A B C 18

19 5 100% 2 2 A A B C if CRR i,24 = 0 y i = 1 otherwise 6 x i ˆµ xi ˆσ xi x i > ˆµ xi + 3ˆσ xi x i < ˆµ xi 3ˆσ xi x i 2 19

20 10% ( )/ /( + ) ( + + )/ ( )/ / ( + )/ / / 6: 21 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 = 1 = 0 7: C 8 9 ROC Receiver Operating Characteristic 16 A B B.1 ROC A

21 A B C McFadden % ROC ROC 0.7 z p LR(8) Log likelihood Prob > LR AIC McFadden s R % McFadden s Radj : C Total : C 21

22 感度特異度 Area under ROC curve = : C ROC Winkelmann and Boes (2006) Greene (2007) Cameron and Trivedi (2005) 0 if CRR i,24 = 0 1 if 0 < CRR i,24 < 0.5 y i = 2 if 0.5 CRR i,24 < 1 3 if CRR i, % C 10 A B B.2 22

23 C McFadden 0.1 z p cut cut cut LR(7) Log likelihood Prob > LR AIC McFadden s R McFadden s Radj : C

24 6.2 5 A 2 Winkelmann and Boes (2006) Greene (2007) Cameron and Trivedi (2005) A.1 2 y i OLS [0, 1] OLS i 1 π i 2 24

25 π i P {y i = 1 x i } = exp {β 0 + β 1 x 1,i + + β k x k,i } 1 + exp {β 0 + β 1 x 1,i + + β k x k,i } = exp { x i β} 1 + exp { x i ( ) β} = Λ x i β (A1) 1 π i = P {y i = 0 x i } = 1 P {y i = 1 x i } = 1 Λ ( ) x i β β = (β 0, β 1,, β k ) x i = (1, x 1,i,, x k,i ) Λ ln L (β; y, x) = n i=1 ˆβ A.2 { ( ) ( ( ))} y i ln Λ x i β + (1 y i ) ln 1 Λ x i β 2 A.2.1 McFadden R 2 2 McFadden R 2 R 2 ln L 0 ln L 1 ln L 0 = 1 ln L 1 ln L 0 L 0 L 1 A.2.2 McFadden R 2 adj McFadden R 2 adj R 2 adj 1 ln L 1 K ln L 0 K A Γ 25

26 p 2 ˆp = Λ ( x β ) c ŷ i 1 if ˆp > c ŷ i = 0 otherwise Γ Γ(c) = 1 P (ˆp c y = 1) (c) = P (ˆp c y = 0) 11 π (A1) (1) (0) (1) π (1 Γ) (1 π) (0) πγ (1 π) (1 ) 11: 2 π (1 Γ) + (1 π) (1 ) A.2.4 ROC c 1 ˆΓ ˆ g() () 1 ˆΓ(c) g (ˆp c y = 1) ˆ (c) g (ˆp c y = 0) ROC 1 ROC (0, 0) (0, 1) (1, 1) 45 ROC area under ROC curve ROC [0.5, 1] 1 B B.1 A B A B

27 z p LR(5) Log likelihood Prob > LR AIC McFadden s R % McFadden s Radj : A Total : A 感度特異度 Area under ROC curve = : A ROC 27

28 z p LR(6) Log likelihood Prob > LR AIC McFadden s R % McFadden s Radj : B Total : B 感度特異度 Area under ROC curve = : B ROC 28

29 B.2 A B z p cut cut cut LR(4) Log likelihood Prob > LR AIC McFadden s R McFadden s Radj : A 24 29

30 z p cut cut cut LR(7) Log likelihood Prob > LR AIC McFadden s R McFadden s Radj : B 24 Araten, Michel, Michael Jr. Jacobs, and Peeyush Varshney (2004) Measuring LGD on Commercial Loans: An 18-Year Internal Study, The RMA Journal, Vol. 86, No. 8, pp Asarnow, E. and D. Edwards (1995) Measuring Loss on Defaulted Bank Loans: A 24-Year Study, The Journal of Commercial Lending, Vol. 77, No. 7, pp Basel Committee on Banking Supervision (2006) Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework - Comprehensive Version. Black, Fischer and John C. Cox (1976) Valuing corporate securities: Some effects in bond indenture provisions, Journal of Finance, Vol. 31, No. 2, pp Cameron, A. Colin and Pravin K. Trivedi (2005) Microeconometrics : methods and applications: Cambridge. Dermine, Jean and Cristina Neto de Carvalho (2006) Bank loan losses-given-default: A case study, Journal of Banking & Finance, Vol. 30, pp Duffie, Darrell and Kenneth J. Singleton (1999) Modeling term structures of defaultable bonds, Review of Financial Studies, Vol. 12, No. 4, pp

31 Franks, Julian, Arnaud de Servigny, and Sergei Davydenko (2004) A Comparative Analysis of the Recovery Process and Recovery Rates for Private Companies in the UK, France and Germany, Technical report, STANDARD & POORS RISK SOLUTIONS REPORT. Frye, Jon (2000) Depressing Recoveries, Risk, pp , November. Geske, Robert (1977) The Valuation of Corporate Liabilities as Compound Options, The Journal of Financial and Quantitative Analysis, Vol. 12, No. 4, pp Giesecke, Kay (2006) Default and information, Journal of Economic Dynamics & Contro, Vol. 30, No. 11, pp Greene, William H. (2007) Econometric Analysis: Prentice Hall, 6th edition. Grunert, Jens and Martin Weber (2007) Recovery Rates of Commercial Lending: Empirical Evidence for German Companies, Working Paper, SSRN. Guha, Rajiv and Alessandro Sbuelz (2002) Recovery of face value at default: Theory and empirical evidence, Working Paper, LBS. (2004) Structural RFV: Recovery Form and Defaultable Debt Analysis, in Proceedings of C.R.E.D.I.T. 2004, Workshop on Validation of Credit Risk Models, GRETA. Hartigan, P. M. (1985) Algorithm AS 217: Computation of the Dip Statistic to Test for Unimodality, Applied Statistics, Vol. 34, No. 3, pp Hartigan, J. A. and P. M. Hartigan (1985) The Dip Test of Unimodality, The Annals of Statistics, Vol. 13, No. 1, pp Hurt, Lew and Akos Felsovalyi (1998) Measuring Loss on Latin American Defaulted Bank Loans: A 27-Year Study of 27 Countries, Journal of Lending & Credit Risk Management, Vol. 81, No. 2, pp Jarrow, Robert A. (2001) Default Parameter Estimation Using Market Prices, Financial Analysts Journal, Vol. 57, No. 5, pp Jarrow, Robert A. and S. Turnbull (1995) Pricing Derivatives on Financial Securities Subject to Credit Risk, Journal of Finance, Vol. 50, No. 1, pp Long, J. Scott and Jeremy Freese (2003) Regression models for categorical dependent variables using Stata: Stata Press, 1st edition. Longstaff, Francis A. and Eduardo S. Schwartz (1995) A Simple Approach to Valuing Risky Fixed and Floating Rate Debt, Journal of Finance, Vol. 50, No. 3, pp Madan, Dilip B. and Haluk Unal (1998) Pricing the Risks of Default, Review of Derivatives Research, Vol. 2, No. 2-3, pp

32 Merton, Robert C. (1974) On the Pricing of Corporate Debt: the risk structure of interest rates, Journal of Finance, Vol. 29, No. 2, pp Winkelmann, Rainer and Stefan Boes (2006) Analysis of microdata: Springer. Zhou, Chunsheng (2001) The term structure of credit spreads with jump risk, Journal of Banking and Finance, Vol. 25, No. 11, pp (2005) Vol. 18 (2005) (2007) (2004) Reduced Form PD LGD ISM Research Memorandum No.911 (2007) EL UL

1 1.1 Merton(1974) Black and Cox (1976) PD Probability of Default LGD Loss Given Default 1 EAD Exposure At Default II Merton (1974) Merton Merton Gesk

y z II 2 :,,,,. UFJ CRD y ed061001@ srv.cc.hit-u.ac.jp z yamasita@ ism.ac.jp 1 1 1.1 Merton(1974) Black and Cox (1976) PD Probability of Default LGD Loss Given Default 1 EAD Exposure At Default II Merton