Ⅰ CAPM VaR WTO

Transcription

1

2 Ⅰ CAPM VaR WTO

3 Ⅱ

4 Ⅲ

5 Ⅳ ABSTRACT The question of how to avoid and control credit risk has long been the major concern for financial institutions and their monitoring departments all over the world. Since the end of the 1980s with the development of financial globalization and the intensified fluctuation in financial markets banks and investments of various countries have been challenged by the problem of unprecedented credit risks in business. The World Bank s research study on the crisis of the world bank industry indicates that credit risk is the major cause for banks to go bankrupt. In China it is commonly known that the credit asset quality in banks of commerce is so poor and the bad loan ratio remains so high that credit risk would constitute the biggest potential financial risk for bank of commerce in China. Besides there exist certain defects in the credit risk management systems in China s banks of commerce. Therefore a careful study on the very subject of the credit risk management in banks of commerce would be highly significant in its theoretical as well as its practical sense. In this regard the author proposes in this dissertation that in credit risk managing practice We need first to evaluate the credit rank of a enterprise by the fuzzy mathematics principles to assess the credit risk of a enterprise by the way of the Typical Discriminant analysis. Then We use the option-pricing model the risk-neutral pricing model and the CAPM method to analyze its capital asset price. At the same time the VaR method the invest portfolio theory and the means of credit quota are employed to decide the degree of the potential credit risk. Noticeably when explo-

6 ABSTRACT Ⅴ ring the question of credit risk game the author avails himself to the static game of incomplete information theory in the study of the credit risk in businesses with debts and works out three valuable instructive prepositions for the credit business. In this dissertation the author also put the dynamic game of incomplete information theory into the study of the classification of credit market types in China and the study of the efficiency in the credit market. The author discusses the tendency for the future development of banks in China by the way of the Douront game and the Stackeberg game. The author also establishes in the dissertation the utility function of the bank manager and analyses the defects and weaknesses existing in the credit capital management system from the perspective view of the utility theory. The author points out that in the process of the gradual progressive mode of Chinese economic reform bank loans have backed up forcefully China s economic growth while at the same time bank credit has been trending the state enterprises. The extremely unbalanced input and output of ownership economic structure has led to the problems of inefficiency in the bank loan distribution the poor match between loan market structure and performance the loss of loan capital and large bad loan. It has also hinders the non-state enterpries to develop healthily and rapidly. The reasons go like this the factors of a double-track system of the loan market the monopoly in the loan market as well as the difference of the attributes of business ownership the asymmetric information and the inperfect monitoring system in bank result in the difficulties in credit financing for the non-state economy. They also cause unideal performances in the state-own banks of commerce and bad bank asset. These consequences in turn trap China s economic advancement. Hence the author argue that with China

7 Ⅵ joins in the World Trade Organization charges will take place in the ownership economy. Under such a condition the petty and middlesized financial institutions in China must be perfected and further developed. In addition the reforms in the state-owned property right system should go into depth. More the development process of convertibility of interests should be quickened. Only in this way can the non-state enterprises compete fairly with the state enterprises in the credit market and only in this way can the credit capital supply meet the demands of the sustained high growth in the non-state economy. In short in the dissertation the author has on the one hand referred to the latest research finding in the corresponding field overseas and on the other hand drawn on knowledge of economy administration mathematics and of operation research in the study of the subject of the credit risk management. Especially the author has done a creative research study in the application of some credit risk management methods. The creativeness can be found in the use the fuzzy mathematical principals to take all the factors of the quality index of enterprise runners the prospect index as well as the treasure index into consideration in the study of the credit scope. Based on a qualitative analysis the mathematical modelization and a comprehensive quantitative assessment of the credibility of a enterprise at different levels can be made. Thus aspects of a enterprise s credibility can be revealed and the general credit level of the enterprise can be judged. These operations will offer banks some instructive ideas when taking constructive strategies in credit management practice. The creativeness is also seen in the application of the game theory to the analysis of effects and influence the performance of main economic bodies

8 ABSTRACT Ⅶ have on the forming credit risk mechanism. The creativeness again lies in the use of the ideas of asymmetric information in information e- conomics to explain the principal-agent relationship between a bank and a enterprise. The asymmetric information between them would cause the adverse selection and moral hazards which would also influence the formation of credit risk mechanism. The creativeness is again found in the investigation of how to use the non-linear programming model to work out the best strategies against credit risk so that the bank can avoid the loan capital being at risk to the largest extent if the bank is able to make a sound judgement as to whether the credit risk of the invested project is high or low. Furthermore there are some creative ideas in putting forward the theoretical calculating method for calculating the credit risk scale and in describing the mathematical relationship between the credit risk and the credibility of a enterprise. There are also degrees of breakthrough in the exploration of how game theory can be used in pricing the bank loan. All these ideas are quite operational and are beneficiary to the credit risk management practice for banks of commerce in China. Key words Credit Risk Loan Pricing Game Analysis Fuzzy Evaluate Credit Management Systems

9 Ⅰ

10 Ⅱ VaR WTO

11 1 40%

12 2 90% WTO

13

14 4 3 4 WTO 5 VaR

15 5 CAPM VaR WTO

16 6 BIS 8%

17 7 5C CART

18 8 CAPM

19 9 J. P. Creditmetrics KMV EDF KMV VaR VaR BIS

20 10 WTO WTO

21 11

22

23

24 14 20

25

26

27 17

28

29

30

31

32

33 %

34

35

36

37

38 28 VaR WTO

39 29

40 30

41

42 J P 2. credit derivatives

43

44

45 C 5C Character Capacity Capital or cash Collateral Condition

46 36 5W 5P 5W Who Why When What How 5P Personal Purpose Payment Protection Perspective 5C 5W 5P CART CART 1984 M. Laurentius James M. patlell Mark A. wolfson CART CART 4

47 Beaver Edward I. Altman 1968 Z

48 38 5 Z-score Zeta Z Z Z 1974 Delton L. Chessen 6 Delton L. Chessen 75% 2 57% Deakin 1972 Edmisterd 1972 Dimond 1976 Ohlson 1980 LOGIT PROBIT Logistic

49 Mortality Rat Model 1993 KMV Expected Default Frequency EDF Kevin Tan 1992 Coat 1993 Altman Marco Varetto J P Credit Metrics VAR

50 40 BZW CCFP

51 41 Beaver 1966 Z Altman 1968 Delton Chessen CART A 1 A 2 A 8 A 1 = a 11 a 12 = A 2 = a 21 a 22 = ~ ~

52 42 A 3 = a 31 a 34 = A 4 = a 41 a 42 = A 5 = a 51 a 54 = A 6 = a 61 a 67 = A 7 = a 71 a 75 = A 8 = a 81 a 84 = 2. AHP 3. Y = AAA AA A BBB BB B CCC CC C AAA AA A BBB BB B CCC CC C AAA AAA 4. A i i = A i i = a ij a ij t Y t r ijt A i R i R i = r i11 r i12 r i1m r i21 r i22 r i2m r in1 r in2 r inm i A 1 A 2 A 8 n A i m

53 A i = W i R i A A i = b i1 b i2 b im W i A i b it M! b it = W i1 r i1t! W i2 r i2t!! W in r int F 1 = P 1 P 2 P 3 P 4 A 1 A 2 A 3 A 4 T P i i = A i i = F 2 = A 5 F 3 = A 6 F 4 = A 7 F 5 = A 8 5. Z

54 44 Z = Z 1 Z 2 Z m = K F 1 F 2 F 3 F 4 F 5 T K F i i = Z j j = 1 2 m M! 6. Z 1999 K = K 1 K 2 K 3 K 4 K 5 = P = P 1 P 2 P 3 P 4 = W 1 = R 1 = ( ) A 1 = W 1 R = ( ) = A 2 = A A = = A 5 =

55 45 A 6 = A 7 = A 8 = F 1 = P A 1 A 2 A 3 A 4 T = F 2 = A 5 = F 3 = A 6 = F 4 = A 7 = F 5 = A 8 = Z = K F 1 F 2 F 3 F 4 F 5 T = AAA AA A BBB BB B CCC CC C % % % 22. 6% % % 6. 93% 2. 95% 3. 07% A

56 % BBB 22. 6%

57 47 5C ALtman Zscore ZETA Meyer and Pifer 1970 Altman 1968 logit Press and Wilson 1978 probit Barth and Brumbaugh 1989 logistic West 1985 Discriminant Analysis Fisher

58 Multivariate Discriminant Analysis Discriminant Analysis DA DA Bayes Fisher LDA 3

59 49 1 n α π α α = 1 k n = k α = 1n α P P R P n k α π α n α π α P x α i i = 1 n α α = 1 k y α = c' x α c = c 1 c P ' P 珋 y α π α y α i 珋 y k y α 珋 y α = 1 n α n α y α i i = 1 珋 y = 1 n k α = 1 n α i = 1 i y α i = 1 n n k α 珋 y α α = 1 K y α i y α T = k α = 1 SST = k α = 1 = k α = 1 = c' Tc n α i = 1 i n α y α i i = 1 n α i = 1 x α i - 珋 y 2 c' x α - c' 珋 x 2 i - 珋 x x α - 珋 x ' y α i i i i

60 50 SS TR = k α = 1 = k α = 1 = c' Bc n α 珋 y α - 珋 y 2 n c' α 珋 x α - c' 珋 x 2 B = k n α 珋 x α - 珋 x 珋 x α - 珋 x ' α = 1 y α i E = k α = 1 SSE = k α = 1 = k α = 1 = c' Ec n α i = 1 n α y α i i = 1 n α i i = 1 x α i - 珋 y α 2 c' x α - c' 珋 x α 2 - 珋 x α x α - 珋 x α ' i SST = SS TR + SSE SST SS TR SSE n - 1 k - 1 n - k K K F = SS TR / K - 1 SSE / n - k F F k α - 1 n - k F F c c c F Δ c = SS TR c' Bc = SSE c' Ec Δ c E - 1 B E - 1 B

61 λ 1 λ 2 λ r > 0 B - λe = 0 c 1 c 2 c r B - λ i E = 0 i = 1 r c i Δ c i = c' ibc i = c' i λ i Ec i = λ c' i Ec i c' i Ec i i = 1 r i c = c 1 SS TR SSE Δ c 1 = λ 1 K Z x = 1 c' 1 x K P Z x = 2 c' 2 x Z x = 3 c' 3 x Z x i P i λ i r r 0 0 < r = λ i / r Z x 1 Z r0 x i = 1 P 1 2 r0 = r 0 λ i r λ i r 0 i = 1 i = 1 75 ~ 95% Z x 1 r 0 Z r0 x π α r 0 Z x 1 Z r0 x 珔 Z α 1 = 1 n α n α c' 1 x α i 珔 Z α r 0 i = 1 r 0 = 1 x = x 1 51 = 1 n α n α x π i Z x - 1 珔 Z i 1 = min 1 j k i = 1 c' r0 x α i α = 1 k x 2 x p ' Z x 1 Z 1 x - 珔 Z j 1

62 52 r 0 > 1 x = x 1 x 2 x p ' r 0 x Z r0 x r 0 D 2 = α Z x - i 珔 Z α i 2 λ i α = 1 k i = 1 x π i = min D 2 i 1 j kd 2 j special treatment ST ST PT ST PT / / x 1 x 2 x 3 x 4 x 5 Z x = c 0 + c 1 x 1 + c 2 x 2 + c 3 x 3 + c 4 x 4 + c 5 x 5 c 1 c 2 c 3 c 4 Z 1 c 5

63 53 n 1 = 56 ST PT π1 n 2 = 72 π2 n = 128 x α i x 1 x 2 x 3 x 4 x SAS 3. 2 Eigenvalue Wilks' lambda Chi-square df Sig R 珔 Z 1 珔 Z Eigenvalue Wilks lambda U Lambda 0 ~ Z珔 α α = F X E-18 1% X E-09 1% X % / X % / X E-11 1%

64 Z D1 D2 T Z D1 D2 T ST A ST ST ST ST ST ST A ST A ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST

65 55 Z D1 D2 T Z D1 D2 T ST ST ST ST ST ST ST ST ST ST ST ST ST ST ST PT A PT PT PT PT PT PT PT Z d1 π1 d2 π2 T d1 < d2 T = 1 π1 d1 > d2 T = 2 π2

66 % Z X = X X X X X 5 1% R = X 2 / X 5 / X 4 X 1 X 3 / π1 π2 Z X r 0 = 1 x = x 1 x 2 x 3 x 4 x 5 Z X x π i Z x - 珔 Z i = min 1 j 2 珔 Z 1 珔 Z 2 π1 Z x - 珔 Z j i = 1 2 π A ST PT π % π2 100% π1 π % %

67 ST PT ST ST PT %

68

69 x 1 r x 1 X x 1 u 1 δ 2 1 N u 1 δ 2 1 f x 1 59 x B r r x 1 B α B B x 1 r

70 60 b Q 1 - α 1 - α = - f x 1 dx B B x δ 2 1 B Ⅰ Ⅱ x 1 J P KMV EDF KMV Creditmetrics + McKinsey McKinsey

71 AAA x 2 = 10 AAA AA x x 2 x 2 u 2 δ 2 2 u 2 δ 2 2 u 2 δ 2 2 x 1 x 1 f x 1 f x 2 BBB

72 62 f x 1 = 1 exp - 1 2πδ 2 槡 1 [ ] x 1 - u 1 δ 1 [ ] f x 2 = exp x 2 - u 槡 2πδ 2 δ 2 2 x 1 x 2 ( ) ( ) X = x 1 u = u 1 x2 u2 X 1 X 2 C = δ2 1 0 C = δ 2 2 1δ 2 2 C C δ2 = 1 δ C 2 0 δ1 X 1 X 2 { [ ] } 1 f x 1 x 2 = exp - 1 x 1 - u x 2 - u 2 2 2π δ 1 δ 2 2 δ x 1 x 2 b 2 Q = P X 1 b 1 X 2 b 2 = b1 - - δ 2 1 f x 1 x 2 dx 1 dx 2 2

73 % 52%

74 64 80%

75

76 66 5

77

78

79 69 4 5

80 70

81 SL DL

82 DL SL E r L 4-1 E 0 r 1 SL 1 DL E 1 SL 1 E 0 r 0 r 2 SL 2 DL E 2 SL 2

83 1 = + + ROE M = ROE L - L C 1 - t M L t C risk premium 73

84 74 1. CAPM 1 CAPM CAPM E ρ δ r π c r 1 β CAPM E ρ - r = βπ 1 - δ 1 + r 1 - r - c = 1 + ρ r 1 r 1 = 1 + 2r + βπ + c δ 2. 2 UL i

85 σ i = UL i = 槡 EDF i 1 - EDF i LGD i EDF i 槡 EDF i 1 - EDF i LGD i 1 δ i EDF i = 0. 18% LGD i = = %. ρ ij = COV ij SD i SD j COV ij SD i i SD j j UL P X i X j i j UL P = N [ ] i = 1 X 2 i UL 2 i + N N i = 1 j = 1 i j X i X j UL i UL j ρ N X i = 1 i = 1 i X i i MRC i dul P MRC i = X i dx i i MRC ij

86 76 UL P1 10 = VaR VaR RN Arrow 1953 Harrison 1979 Pliska 1981 Kreps

87 10% B 15. 8% p k 1 = 1 + i 1 p k i 1 LGD = 1 p 1 p 1 = 1 + i 1 = 1. 1 = k p 1 p 1 = 1 - p 1 = = n 2 p i 2 2 = 1 + i f 1 77

88 78 i 1 i f 1 = 1 + i = = i f 1 = 12% 1 + c 1 = 1 + k = = k k 1 k 2 B c 1 = 20. 2% p c 1 = 1 + f 1 p 2 = 1 + f = = c p 2 = 1 - p 2 = p 3 p 4 p n Ginzberg et al Belkin et al φ 1 LGD φ 1 = p 1 LGD φ 1 ε 1 u 1 φ 1 = ε 1 + u 1

89 ε 1 t 1 LGD ε 1 = t 1 LGD u 1 LGD p 1 LGD = t 1 LGD + u 1 LGD p1 t 1 φ 1 = 1% LGD = 40% t 1 = 1% φ 1 = p 1 LGD = t 1 LGD + u 1 φ 1 = p = u 1 = p 1 u 1 p 1 = 2. 5% t 1 = 1% u 1 = 0. 6% s s p 1 E NPV = 1 - p r + s + p1 1 - LGD = r r = 4% = 6. 5% LGD = % s E NPV = =

90 80 s % L k r LGD L L 1 1 > L s s p k = 1 + r p 1 = 1 - p p 1 L + r + s + p1 1 - LGD = L 1 + r 1 1 t = 0 D 0 t = T D r L D = D 0 e r L T V t t T 1 D V T

91 81 D 2 D > V T V T min D V T T C = max 0 V T - D D V t Merton V t dv/v= αdt + σdz α σ 2 dz Black-Scholes C C = VN h 1 - De - rt N h 2 D 0 = V- C D 0 = De - rt 1 /d N h 1 + N h 2 = f V D r σ T T d d = De - rt /V T r N h h h 1 = σ2 T - ln d /σ 槡 T h 2 = σ2 T + ln d /σ 槡 T

92 r L r s s = r L - r = - 1 /T ln 1 /d N h 1 + N h 2 s T = 1 r = 5% d = 90% σ = 12% D = h 1 h 2 h 1 = ln 0. 9 = h 2 = ln 0. 9 = N h 1 = N h 2 = D 0 = De - rt 1 /d N h 1 + N h 2 = = = s = r L - r = - 1 /T ln 1 /d N h 1 + N h 2 = - 1 ln = 1. 33%

93 83 i 0 i 1 L T i 0 - i 1 L T i 0 - i 1 L T i 0 - i 1 L T i 0 L T

94 84 i 0 - i 1 L T - i 0 - i 1 L T i 0 - i 1 L T - i 0 L T % ~ 5% 2 3% ~ 5%

95 t = 0 x 2 t = 1 p 3 4 a - a a - b 5 c a - c - a + c - x a - c - b + c - x 4-2 a - c > 0 - pa < p - a + c - x p - x x < pc a - c < 0 - pa < p - x p - x x < pa x < p min a c a - c > 0 x p

96 c a - c < 0 x p a

97 87 1 I W W < I B B = I - W> 0 R r i i = 1 i =

98 88 γ i = r i C i q i C i i C i q 0 i q i 1 i q i = 0 i 0 < q i < 1 i q i = 1 i ρ 0 < ρ < r i k 0 < k < 1 t 0 < t < 1 s 0 s i i < 1 p 0 i < p i < i R i i R f = 0 p i R i p i R f = R 0 < p 1 < p 2 < 1 σ r 1 σ r i C i q i σ = F r 1 r 2 C 1 C 2 q 1 q 2 q i i i q i B q i R q i C i 1 q i = 0

99 W+ kc i r i B 0 σ = 1 + ρ B r i B = ρ - r i B 2 i q i = 1 i 1 + r i B - R i + kc 1 > 0 σ = kc i r i B 3 0 < q i < 1 Ⅰ i kc i r i B 0 R i + kc i r i B 0 i σ = 1 - q i 1 + ρ B r i B = 1 - q i ρ - r i B Ⅱ i 1 + r i B - kc i > r i B - R i + kc i 0 σ = q kc i i r i B q R 1 - p s r 1 B p 1 s 1 C ρ W q R 2 - p r 2 B p 1 C ρ W q R 2 - p s r 2 B p 2 s 2 C ρ W 89

100 90 q R 1 - p r 1 B p 2 C ρ W q p r 1 B p 1 kc ρ B 0 q p r 2 B p 2 kc ρ B 0 q R 1 - p s r 1 B p 1 s 1 C ρ W 0 q R 2 - p s r 2 B p 2 s 2 C ρ W 0 t minσ = t q kc r 1 B q 1 ρ - r 1 B t q kc r 2 B q 2 ρ - r 2 B s. t. q R 1 - p s r 1 B p 1 s 1 C ρ W q R 2 - p r 2 B p 1 C ρ W q R 2 - p s r 2 B p 2 s 2 C ρ W q R 1 - p r 1 B p 2 C ρ W q p r 1 B p 1 kc ρ B 0 q p r 2 B p 2 kc ρ B 0 q i = 0 i = 1 2 i i = 1 q i 0 s i = 0 i

101 q i = 1 i = 1 2 s i = 1 i = 1 2 i 100% q i = 0 0 < s i < 1 i = 1 2 Kuhn-Tucher - t + λ 1 q 1 p s 1 - λ 2 q 1 p 2 - λ 3 q 1 p 1 = t - λ 1 q 2 p 1 + λ 2 q 2 p s 2 - λ 4 q 2 p 2 = 0 tk + λ p 1 s 1 - λ p 2 - λ p 1 k = t k - λ p 1 + λ p 2 s 2 - λ p ρ k = 0 - t 1 + ρ B - kc 1 - λ R 1 - p s r 1 B p 1 s 1 C ρ W + λ R 2 - p r 1 B p 2 C ρ W - λ p r 1 B p 1 kc ρ B = t 1 + ρ B - kc 2 + λ R 1 - p r 2 B p 1 C ρ W - λ R 2 - p r s 2 B p 2 s 2 C ρ W - λ p r 2 B p 2 kc ρ B = 0 λ 1 q R 1 - p s r 1 B p 1 s 1 C ρ W q R 2 - p r 2 B p 1 C ρ W = 0 λ 2 q R 2 - p s r 2 B p 2 s 2 C ρ W q R 1 - p r 1 B p 2 C ρ W = 0 λ 3 q p r 1 B p 1 kc ρ B = 0 λ 4 q p r 2 B p 2 kc ρ B = 0 λ 1 λ 2 λ 3 λ 4 0 Lagrange C 1 = C 2 Kuhn-Tucher 91

102 92 r k a - b R ρ W+ dt 1 + ρ B 1 = - 1 k ap s 1 - bp 2 B C 1 + ρ 1 = B k q td 1 = kap s 1 - kbp 2 r k a - b R ρ W+ d 1 - t 1 + ρ B 2 = - 1 k ap 1 - bp s 2 B C 1 + ρ 2 = B k q 1 - t d 2 = kap s 2 - kbp a = 1 - p 2 ts t b = 1 - p 1 t t s 1 1 d = 1 - p p s 1 s 2 C 1 = C 1 + ρ 2 = B k

103 q 1 q 2 W q i B R t p i s i r 1 r 2 r 1 > r 2 93

104

105 r P 1 R 1 P P 2 2 < P 1 R R 2 2 > R 1 R 1 - r r + 1 ( R 2 - r r + 1 ) 1 + r - 1 ( 1 + r - 1) ( ) P P P P 2 2 ( ) P P P E 1 = max R 1 - r - 1 P r 1 - P 1 i R 2 - r - 1 P r 1 - P 2 i = 1 2 = max R 1 P 1 - r + 1 R 2 P 2 - r i R 1 u 1 u 1 = R 1 P 1 u 2 = R 2 P 2 E 2 = max 2 + r P r P 2-1 i = 1 2 i P

106 96 P 1 > P 2, E 2 = 2 + r P u 1 > u 2 E 1 = R 1 P 1 - r + 1 E 2 = R 2 P 2 - r I r R T P R P R R = T R P C R - I 1 + r - C Y= P R - I 1 + r P C 0 R

107 R > R P R R = T P P P P P R r I P C = 0 P R = T P T - C = I 1 + r - C R I 1 + r - C = T T - C P 0 1 f P F P P r Pf P dp 珔 P = P 0 P r = P f P dp 0 P r P f P Pf P dp = P 0 F P P F P - F P r 0 F P 2 Pf P dp T - C I = r I - C 2 f P F P 2 P F P - P 0 Pf P dp f P F P 2 P F P - P Pf P dp > 0 P T - C I 0 r 1 + r I - C 2 T > C P r < 0 97

108 98 1 IR IC C

109 C R 1 - r r r - 1 ( R 2 - r C - r +1 + C ) ( 1 + r + C - 1) E 1 = max R 1 P 1 - r + 1 R 2 P 2 - r C i = 1 2 i E 2 = max 2 + r P r + C P 2-1 i = 1 2 i IR 2 + r + C P r P IC R 1 P 1 - r + 1 R 2 P 2 - r C r P 1 - P C C R 2 P 2 - R 1 P r P C = max 1 - P 2 { R 2 P 2 - R 1 P 1 P } 2 C P 2 99

110 i P i P i 2 P i R i 3 r r 0 4 C i S E d E d = P R i i - r P i C i R i - r C i E d 0 i E l E l = P i r P i SC i - i E l 0 i E l = 0 r = i P i SC i /P i E d = P i R i - i P i 1 - S C i

111 101 i S E d P i R i C i P i R i E d P i C i P i C i E d 0 E d 0 C i P i R i - i / 1 - P i 1 - S P i P i R i = 0. 2 i = 0. 1 S = % 2. 5 C i = % C i =

112 102 1.

113 r d r 0 r L r 0 r 0 - r L r L - r d S S' A B r L - r d r 01 - r L Q 1 Q 0 r 0 - r L

114 104 r L r

115

116 J P Creditmetrics KMV EDF KMV Bankers Trust Risk Adjusted Return On Capital RAROC Creditmetrics 1997 J P Creditmetrics 1

117 Transition Matrix 2 VaR 3 E r p = n σ 2 P = n i = i = 1 w 2 i σ 2 P w i E r i = n i = 1 i j n w i w j Cov r i r j j = 1

118 108 4 KMV KMV KMV Creditmetrics 1 EDF Expected Default Frequency KMV ~ 5 EDF 2 Default Point EDF

119 109 3 EDF EDF KMV 4 KMV = EDF 1 EDF EDF Distance to Default DTD = AV - DP /AV DTD Distance to Default AV

120 110 Asset Value Debt Equity DP Default Point EDF EDF = DTD/SD = AV - DP /AV/SD SD DTD DTD 30 20% SD % % DP EDF AV

121 111 RAROC Risk Adjusted Return On Capital RAROC MPT RAROC RAROC = RAROC RAROC RAROC RAROC 1. RAROC = RAROC RAROC

122 112 1 ΔL L = - D ΔR L 1 + R L ΔL/L D L R L ΔR ΔR = max Δ R i - R G > 0 Δ R i - R G i R i R G RAROC ΔL = - D L L ΔR/ 1 + R L 2 RAROC LGD AA AA

123 0. 03% % σ 3. 4 σ N N i = 1 p 1 i - p i σ = p 槡 N i AA i W i = 3. 4 σ i LGD i F F i i 3. RAROC RAROC RA- ROC Capital Asset Pricing Model CAPM RAROC CAPM R i - R f = β R i m - R f R i i R f R m β i i β i = σ im = ρ imσ i σ m = ρ imσ i σ 2 m σ 2 m σ m β i σ im R i R m σ m R m ρ im R i R m ρ im σ m σ i = σ im R i - R f = ρ im σ i R m - R f σ m 113 R i - R f ρ im σ i = R m - R f σ m

124 RAROC ρ im = 1 RAROC R i - R f /σ i R i - R f 4. RAROC 1 RAROC RAROC RAROC 2 RAROC VaR 1993 BIS 1995

125 BIS VaR VaR VaR VaR VaR 8% VaR VaR 1 1. VaR 115 VaR Value at Risk VaR VaR x% VaR R f R c R Prob R < R = R - f R dr = c VaR VaR = - R W VaR VaR = - R W+ μw 1. VAR

126 116 μ W VaR 2. VaR P t R t P t R t R t = P t - P t - 1 /P t - 1 P t - 1 R t R t ~ N μ δ 2 t Z t = R t - μ /δ t Z t Z t ~ N 0 1 Prob R t < R = Prob Z t < R - μ /δ t = c c α R - μ /δ t = α R = μ + αδ t VaR VaR = - μw- αδ t W VaR = - αδ t W VaR % ~ 99. 9% VaR VaR VaR

127 117 1 P σ VaR P P P σ P σ VaR P σ J P 1997 VaR VaR VaR 6% 100 BBB 1. KMV BBB BBB 1. VAR

128 % A CCC BBB AAA 0. 02% AA 0. 33% A 5. 95% BBB % BB 5. 30% B 1. 17% CCC 0. 12% Default 0. 18% 2. 5 C C P = C r 1 + s r 2 + s 2 + C r 3 + s 3 3 C + F r 4 + s 4 4 C F r i s i BBB i = C = 6 F = 100

129 BBB A 6 P = = BBB AAA AAA AA A BBB BB B CCC Default VaR BBB VaR

130 120 1 VaR VaR BBB % VaR = % VaR = VaR VaR 2 VaR % 5% VaR = % 1% VaR = % 1% VaR VaR VaR 1. 47% % % % VaR =

131 % BIS 8% VaR 1% VaR BIS VaR 1% VaR BIS VaR VaR BIS BIS AAA CCC 8% AAA VaR BIS BIS VaR n R i t i = 1 n R t = R t 1 R t 2 R T n R t F = ρ i j n n n ω = ω 1 ω 2 ω n T

132 5. 3 BBB VaR % = = = AAA AA A BBB BB B CCC Default σ = = } 5% VaR = σ = % VaR = σ = } 5% VaR = 95% = = % VaR = 99% = = % VaR 5. 3% % % % 5% VaR 1. 47% VaR 1. 17% % % 1% VaR

133 ω 1 + ω ω n = 1 R t P R t P R t = P ω 1 R t + 1 ω 2 R t ω n R t n R t P VaR VaR VaR P = - αδ P W δ P R t P R t P δ P δ i δ 2 P δ 2 P = N = ω 1 ω 2 ω n δ ρ 1 2 ρ 1 n δ ω 1 0 δ 2 0 ρ ρ 2 n 0 δ 2 0 ω δ n ρ n 1 ρ n δ n ωn i = 1 ω2 i δ 2 i + N i = 1j N = 1 i j ω i ω j ρ ij δ i δ j δ 2 P = ω T δfδω VaR P VaR i VaR P = - αδ P W= - α ω T δfδω 1 2 W = 槡 - αω 1 Wδ 1 - αω 2 Wδ 2 - αω n Wδ n T F - αω 1 Wδ 1 - αω 2 Wδ 2 - αω n Wδ n 槡 123

134 124 T = VaR 1 VaR 2 VaR n F VaR 1 VaR 2 VaR n 槡 T = 槡 VaR F VaR VaR = VaR 1 VaR 2 VaR n ω i W i VaR δ ij i j δ ij = ρ ij δ i δ j ρ ij ρ ij ρ ij 珔 R P δ 2 P ω i

135 125 VaR VaR WTO VaR VaR VaR r i S i VaR VaR VaR VaR

136

137 127 I W W < I - W= B r ρ R R > 1 + ρ B + W P 0 < P < 1 Y Z X Q Q = f T S T S

138 a δ B 1 + ρ R B α B B 5. 3 Q 1 - α 5. 3 B B 5. 3 δ 2

139 B 2. Z b Q v Q Z = bq v Q b v Z' = bvq v v > 1 3.

140 130 X c Q r Q X = c 1 - Q r Q c r X' = - rc 1 - Q r - 1 r > X Z M Q e 0 Q e v > 1 r > 1 v > 1 r > b c

141 1 b = c = 0 Q X = 0 Z = 0 2 b < 0 c < 0 Q X Z 3 c > b > 0 Q = 0 X = c Z = 0 Q = 1 X = 0 Z = b b c 5. 4 X Z 0 Q 1 b > 0 c > 0 b > c v > 1 r > M M 0 Qe 5. 4 X Z 1

142 Q e M X = Z c 1 - Q r = bq v 0 Q 1 b > 0 c > 0 b > c r > 1 v > 1 Q e

143 133

144 N = r θ 1 θ 2 1 Ω = θ 1 θ 2 θ 2 < θ 1 θ Ω 1 1 θ 2 P θ = θ 1 = p P θ = θ 2 = 1 - p 3M = m 1 m 2 1 m = m 1 1 θ 1 m = m 2 1 θ 2 4 m i i = A= W S a = W a = S C

145 135 5 B 2 B 1 X 6 I 1 I 2 θ = θ 1 m = m 1 u θ i m a i = 1 2 u θ 1 1 m 1 S = I 2 - R - B 1 u θ 2 1 m 1 S = R - C u θ 1 1 m 1 W = - B 1 u θ 2 1 m 1 W = - C u θ 1 2 m 1 S = I 1 - R - B 1 - X u θ 2 2 m 1 S = R - C u θ 1 2 m 1 W = - B 1 - X u θ 2 2 m 1 W = - C u θ 1 2 m 2 S = I 1 - R - B 2 u θ 2 2 m 2 S = R - C u θ 1 2 m 2 W = - B 2 u θ 2 2 m 2 W = - C I 1 X > B 2 - B 1 { 2 m θ = m 1 θ = θ 1 1 m 2 θ = θ

146 X B 2 - B 1 m θ a θ p θ m I m θ = m 1 θ Ω a m S m M P θ 2 m 2 = 1 P θ 1 m 2 = 0 P θ 1 m 1 = p P θ 2 m 1 = 1 - p 1 2 P θ 1 m 1 = P θ 2 m 2 = 1 P θ 1 m 2 = P θ 2 m 1 = 0 2 a m A max a = W S θ = θ 1 u θ 2 m a P θ m θ 2 m = m 1 u θ 2 m 1 a P θ m 1 θ 2 = max u θ 2 1 m 1 a P θ 1 m 1 + u θ 2 2 m 1 a P θ 2 m 1 max a = W S θ = θ 1 a = W S = maxu θ 2 1 m 1 a a = W S = max u θ 2 1 m 1 W u θ 2 2 m 1 S

147 = max - C R - C = R - C a m 1 = S m = m 2 u θ 2 m 2 a P θ m 2 θ 2 = max u θ 2 1 m 2 a P θ 1 m 2 + u θ 2 2 m 2 a P θ 2 m 2 max a = W S θ = θ 1 a = W S = max u θ 2 2 m 2 W u θ 2 2 m 2 S = max - C R - C = R - C a m 2 = S 1 2 a m S m M 2 a m S 1 m θ M u θ 1 m S θ = θ 1 max m = m 1 u θ 1 1 m S = max u θ 1 1 m 1 S u θ 1 1 m 2 S m 2 = max I 2 - R - B 1 0 = I 2 - R - B 1 m θ 1 = m 1 θ = θ 2 max m = m 1 u θ 1 2 m S m 2 = max u θ 1 2 m 1 S u θ 1 2 m 2 S = max I 1 - R - B 1 - X - R - B 2 X > B I 1 - B 1 I 1 - R - B 2 m θ 2 = m 2 1 θ 2 θ 1 X

148 138 B 2 - B 1 { m 2 2 m θ = m 1 θ = θ 1 θ = θ 1 B X B 2 - B 1 1 m θ = m 1 2 P θ 2 m 2 = 1 P θ 1 m 2 = 0 P θ 1 m 1 = p P θ 2 m 1 = 1 - p 2 a m A u θ 2 m a P θ m θ 2 m = m 1 max a = W S θ = θ 1 u θ 2 m 1 a P θ m 1 θ 2 = max u θ 2 1 m 1 a P θ 1 m 1 + u θ 2 2 m 1 a P θ 2 m 1 max a = W S θ = θ 1 a = W S = max pu θ 2 1 m 1 W p u θ 2 2 m 1 W pu θ 2 1 m 1 S p u θ 2 2 m 1 S = max - pc p C p R - C p R - C = R - C a m 1 = S m 1 = m 2 A 2 a m 2 = S 2 a m S 2 a m S 1 m θ M u θ 1 m s θ = θ 1 max m = m 1 u θ 1 1 m S = max u θ 1 1 m 1 S u θ 1 1 m 2 S m 2 = max I 2 - R - B 1 0 = I 2 - R - B 1

149 139 m θ 1 = m 1 θ = θ 2 max m = m 1 u θ 1 2 m S = max u θ 1 2 m 1 S u θ 1 2 m 2 S m 2 = max I 1 - R - B 1 - X I 1 - R - B 2 X < B 2 - B 1 I 1 - R - B 2 - X m θ 2 = m 1 1 m θ = m 1 θ 2 θ 1 X B 2 - B 1 m θ a θ p θ m I a m S

150 140 1.

151 141 θ i i = 1 2 r θ 2 X θ P ~ 63..

152 142 B i i = 1 2 B i i = 1 2 θ 2 B 2 X B 2 X X B 2 - B 1

153 143 A 1 2 3

154 144 50% - 60% 1 M. Jensen and W. meckling 1976 P. Aghion and P. Bolton 1992 S. A. Ross 1977 S. C. Myers and N. S. Majiluf 1984 P. Asquith and D. Jr. Mullins

155 145 I m X R R b c r R X + R 1 + r

156 146 - X + R 1 + r X X X + m X X m λ 1 - λ θ X + R 1 + r b 1 - θ X - X + m - X - R 1 + r c - X - m θ 1 - θ λ 1 - λ E θ 1 λ = θ λ x + R 1 + r λ x + R 1 + r θ λx λ - x

157 E θ 1 λ = θ 2λR 1 + r - R 1 + r + 2λ - 1 x θ E θ 1 λ = 2λR 1 + r - R 1 + r θ E θ 1 λ = 0 λ λ = 1 2 E θ 2 λ = λ bθ + xθ - cθ - x + mθ + cθ - m λ E θ 2 λ = bθ + xθ - cθ - x λ bθ + xθ - cθ - x = 0 E θ 2 λ = 0 θ θ x = b + x - c 147 Nash θ λ = x b + x - c 1 2 x 1 2

158 148 1 W E θ 1 λ = θ λ x + R 1 + r - w λ x + R 1 + r θ λx λ - x E θ 1 λ = θ 2λR 1 + r - λw - R 1 + r + 2λ - 1 x θ R 1 + r λ = 2R 1 + r - w W > 0 2R 1 + r - W < 2R 1 + r λ > x θ = b + x - c x θ x b - c θ' x = b + x - c 2 θ x 2

159 149 3 a δ B X r R B α B B 1 - α 6. 2 B B 6. 3 δ 2 B 6. 2

160 150 1.

161

162 152 WTO WTO WTO WTO

163 WTO n 1 Dournot. game WTO q i 0 i c q i i = c i q i r = a - b n i = 1 q i a b r c i i π i 153 = q i a - b n i = 1 q i - c i q i i = n π i = a - c i q i - b q 1 q i + q 2 q i + + q 2 i + + q n q i q i π i = 0 i = n q i n n q 1 q 2 q n q i

164 154 π Q = n q i = na - c 1 - c c n i = 1 b n + 1 r = a + c 1 + c c n n + 1 i π i = a + c c i c i c n - nc i 2 b n n π = n π i i = 1 = n i = 1 a + c c i c i c n - nc i 2 b n Ⅰ c i < c j c i q i > q j π i > π j WTO 15% 10% 1 /3 Ⅱ c i = c j = c c π q 1 = q 2 = = q n = a - c b n

165 Q n a - c = b n + 1 r = a + nc n + 1 π i 155 a - c 2 = i = n b n π n a - c 2 = b n Q r n Q n = a - c b 1 n + 1 > 0 2 r n = c - a n + 1 < 0 2 WTO 1 μ μ = Q a - r 2 = b Q 2 2 = n2 a - c 2 2b n

166 156 B B = π + μ a - c n n = b n n = 1 Q = a - c 2b r = a + c 2 π a - c 2 = 4b μ a - c 2 = 8b B 3 a - c 2 = b π π B B WTO π i π n

167 157 WTO Q Q r r u u WTO n Stackelberg Game q l n - 1 q f c 1 c 2

168 158 maxπ q f f q l = q f a - b q l + n - 1 q f - c 2 q f q f = a - c 2 - bq l b n - 1 maxπ q l l q f = q l a - b q l + n - 1 q f - c l q l maxπ q l l q f = q l a - b q l + a - c 2 - bq l - c q l 2b 1 q l = a + c 2-2c b q f = a - 3c 2 + 2c 1 4b n - 1 Q s = q l + n - 1 q f = 3a - 2c 1 - c 2 4b r s = a + 2c 1 + c 2 4 π q l l q f = a + c 2-2c 1 2 8b π q f l q f = a - 3c 2 + 2c b n - 1 q l > q f π q l l q f > π q f l q f

169 159 1 WTO WTO 1. 1 r 2 r r D L 3 α 4 C L D

170 160 C D > 0 C L > 0 5 L r L L r L < 0 r L 6 D r D D r D > 0 r D 2. 1 π π D L = r L - r L r L + r 1 - α - r D D r D - C L r L D r D { π L = r L - r - C L L D = 0 π D = r 1 - α - r D - C D L D = 0 r L = r + C L L D r D = r 1 - α - C D L D

171 r L r L r D r D ROE / / / 2. 1% 5. 5% % 3. 4% 4. 9% % 22% 11% % 24% 8% % 1. WTO

172 % 28% 3. WTO

173 WTO 40% 5. WTO

174 164 WTO WTO WTO

175 165

176 %

177 % 38% 1. U M X Y e = U M + 1 U X + 2 U 3 Y- C e U' M > 1 0 U' X > 2 0 U' Y > 3 0 C' e >

178 168 M U M 1 U M 1 α U X 2 U Y 3 e C e X + Y= W W 2. X Y 1 z = dz = μx + ky dt μ X k Y 0 μ k 1 k < μ 3. Y e e e θ 5 p = e

179 169 θ S p = βp β ρ θ 0 σ 2 C e = 1 2 be2 b > 0 w = s p - C e = β e + θ be2 Arrow-Pratt 1 2 ρvar s p = 1 2 ρvar βθ = 1 2 ρβ2 σ 2 w = E w ρβ2 σ 2 = βe be2-1 2 ρβ2 σ dw w e de = β - be dw de = 0 e = β b β w = 1 2b β2-1 2 ρβ2 σ 2 β e e Y W

180 170 Y e X + Y = W X z = dz = μx + ky dt X X X Y t > 0 Y t = 0 z t = μ X t z t > 0 4. U X 2 U Y 3 U' Y > 3 0 e β b Y U M X Y e U' X > 2 0 X U M X Y e X X Y U X 2 U Y 3

181 p z p' p" > 0 z U M X Y e z D = U M + 1 U X + 2 U Y - 3 C e - p z + U D U' M > 1 0 U' X > 2 0 U' Y > 3 0 C' e > 0 U' D > 5 0 M M D X Y W X + Y+ D = W

182 172 2 X Y z = dz = μx + ky dt 3 e U Y - 3 C e 1 2b β2-1 2 ρβ2 σ 2 0 β b Y k Y Y U X > 2 p z X U X < 2 p z X X X 5 D

183 173 6 X Y D 1.

184

185

186 H. Demsetz 50%

187 CR n HHI - HKI Lorenz Curve Gini Coefficient CR n CR n n 4 8 Herfindahl Index H CR n CR n = n i = 1 X i / X i i = 1 n X i H = n 177 i = 1 X i /T 2 T n X i CR n H

188 178 CR n H CR n 1 n 4 60% % 70% CR n CR 8 70% 40% CR 8 < 70% 20% CR 8 < 40% CR 8 < 20% WTO

189 CR n n = 4 % ~ ~ 2000 H H 0 H = 1 H 1 /n n 0 H 7. 2 H H 1997 H 1997

190 ~ 1999 H ~ ~ 2000 CR n 1995 ~ % % % 4. 57% 0. 40% % 2. 88% 7. 1 WTO

191 % 65% 60%

192 182 90% 1. 2.

193

194 Smirlock 1985 Evanoff Fortier %

195 90%

196 Bai J t t t J t WTO

197 % % GDP Y X lny t = lnX t Adjusted R-squared = Durbin-Watson = F-statistic = t 1 Y t dy t dt 1 dx t - 1 = X t - 1 dt dy t Y t dx t - 1 X t - 1 = GDP

198 CPI RPI 18. 8% 18. 5% CPI 14. 7% 24. 1% 17%

199 7. 4 % GDP % ~ 2000

200 % % 90%

201 191 40% / % % 2. 94% % % % 1 100%

202 % % Y i X it 1984 ~

203 R2 adj DW F Sig. -F lny 0t = lnX 0t lny 1t = lnX 1t lny 2t = lnX 2t lny 3t = lnX 3t lny 4t = lnX 4t ~ 2000 Y i it = X it - i 1 = t t

204 Ⅰ Ⅱ Ⅰ Ⅰ Ⅱ Ⅱ Ⅱ ~

205 GDP % % % 1994 GDP % 22% 48% 53% % % 20% 30% 15% 45% /3 7. 6

206 % % a a b b a b ~

207 % 24. 3% % % 41% % 7. 9% 6. 4% 17% % - 20%

208 GDP GDP 1998 GDP % % % a % 12% 9% b % 18% 14% c % 20% 18% d % 25% 25% e % 33% 35% a b c d e J ~

209 %

210 % 1983 Lipsey and Bocaster % % 1992

211 % % 0. 10% 4. 37% 48. 1% % % % % %

212 WTO %

213 Banerjee

214 % % % 63% GDP 100% 80% % 80% Information A

215 205 symmetry Adverse Selection Moral Hazard Hidden Information Hidden Action Macmilan 1931 Financial Gap

216 206

217

218 %

219

220 % % 40% 40%

221 211 Stiglitz and Weiss 1981

222 212 WTO 1.

223 WTO Mckinnon 1973

224

225 % 7% 1. 70% 90% 2.

226 %

227

228

229 219 4 Asset-Backed Securities ABS ABS ABS ABS ABS ABS ABS 3.

230 220 4.

231 221 1.

232 WTO

233 223 40% 3. 1 D g d g GDP B GDP t

234 224 B t = D g d t GDP 1 + g t g d < g t B t = D g d t 0 GDP 1 + g t B t

235 225

236 226

237 227

238 228 1 Altman E I. Financial ratios discriminate analysis and the prediction of corporate bankruptcy J. Journal of Finance Vol. XXIII 2 Amano M. Credit rationing of a Bayesian Bank with simple screening technologies J. Japan and the World Economy Anthony Saunders. Credit Risk Measurement. M. New York John Wiley& Son Black F Scholes M. The pricing of options and corporate liabilities J. Journal of Political Economy Brian J. Hall and Kevin J. Murphy. Optimal Exercise Prices for Executive Stock Options. American Economic Review Banerjee A V Besley T Guinnane T W. Thy neighbors keeper The design of a credit cooperative with theory and a test. Quarterly Journal of Economics Berger A N Kashyap A K Scalise J M. The transformation of the US banking industry what a long strange trip its been. Brookings Papers on Economic Activity Berger A N Udell G F. Universal banking and the future of small business lending. In Saunders A. Walter I. Eds. Universal Banking Financial System Design Reconsidered. Irwin Chicago IL Berger A N Saunders A Scalise J M Udell G F. The effects of bank mergers and acquisitions on small business lending. Journal of Financial Economics Bester H Sreening vs. Rationing in credit markets with imperfect information J. American Economics Review Besanko D. Thakor A V. Collateral and rationing sorting equilibria in mo-

239 229 nopolistic and competitive credit markets J. Economic Review Coats P Pant L. Recognizing financial distress patterns using a neural network tool M. Financial Management CreditMetrics. Technical document M. J P Hull J C White A. The impact of default Risk on the prices of options and other derivative securities J. Journal of Banking and Finance KMV Corporation. Credit Monitor Overview J. San Francisco California J P Morgan. CreditMETRICS Technology Document R. 1st Edition Internet http / /www. jpmorgan. com Stiglitz J E Weiss A. Credit rationing in markets with imperfect information J. American Economic Review Yellen J L. The new science of credit risk management at financial institutions J. Federal Reserve Bank of Minneapolis the Region J J M J J M ST J

240 M J VaR J M J J VAR M J VaR J J J J J M M M. 1999

241 J M M J M M J M J J J WTO J J J J. NO. C M. 2001

242 M J J J J VAR J J J M M J J J VaR J M J M Ⅰ J

243 233 Ⅱ J J M M M M J J M M E.. M M J J J J J M M. 2001

244 J J J M J M J J J J J M J J J WTO J M. 1998

245 M M J J J J J J WTO J J J M M B I.. M J J M J J

246 M J M M J M J J J J J J J J J J J J J

247 J J WTO J J