Abstract JP Morgan CreditMetrics (1) () (3) (4) 1 3 3 4 4 5 10 6 16 1
1 BIS 1 3 1 BIS 1 BIS 1 3 ALM (1) Value at Risk () (3) RAROC (Risk Ajusted Return On Capital) (4)
3 5 6 31 99% (= p ) ~x X Prf~x Xg = p p p 99% 1% 3 4 1 [4] 3 3
100 A 100 A 100 1 100 100 1 100 0 80 075 4 1 0 1 1 [18] 4 () 4 (1) () (3) (4) RiskMetrics [5] 41 ( ) 4
3 [4] () i i ~r i;y ~r i;y = (1 + R i;y ) (1 0 d ~ i;y ) 0 1 (1) R i;y = i y ~d i;y = i y r i;y d i;y [1, 10, 19] () E[r i ] () ri ri ;r j ( ) () portfolio portfolio = x 0 6x 6 = r i x = 4 5
1: Aaa Aa A Baa Ba B 70 00 00 00 03 84 16 71 00 00 00 00 15 00 7 00 00 00 00 05 118 73 00 00 00 05 05 34 74 00 00 00 00 00 69 75 00 00 00 00 16 30 76 00 00 00 00 11 00 77 00 00 00 03 06 88 78 00 00 00 00 11 53 79 00 00 00 00 05 00 80 00 00 00 00 00 44 81 00 00 00 00 00 41 8 00 00 0 03 6 83 00 00 00 00 10 60 84 00 00 00 06 05 73 85 00 00 00 00 0 87 86 00 00 00 11 19 116 87 00 00 00 00 6 53 88 00 00 00 00 15 57 89 00 03 00 05 7 86 90 00 00 00 00 33 19 91 00 00 00 0 51 131 9 00 00 00 00 0 61 [9] 3 3 (1) 3 4 t n n + 1 X n n + 1 h n = Prfn X n + 1g () X 6
h(t) = h(t; z) = h 0 (t) expf 0 zg (3) z = ( ) = h 0 (t) = 1 3 GDP GDP h 0 4 i L ~ i 3 4 [4, 7] L ~ P ~ i L i P ~ i L i 4 L ~ i i 7
1 i D 0 p i1 p i p id t 0 1 t p i1 p i p id T 0 1 T 1 P 1: 43 1 ( ) t i q i;t q i;t+1 = DX j=1 p j;i q j;t (4) q t = P = p i;d = 0 B @ 0 B @ q 1;t q ;t q D;t q t+1 = Pq t (5) 1 C A p 1;1 p ;1 111 p D;1 p 1; p ; 111 p D; p 1;D p ;D 111 p D;D ( 0 (i 6= D) 1 (i = D) 1 C A i + k i i + j (k > j > 0) i p i+j;i > p i+k;i (k > j > 0) (6) [6, 19] (6) i L ~ i L P ~ i L i 8
4 5 P P L ~ i CreditMetrics 44 V dv = V dt + V dz (7) 5 z [3, ] 1 (7) i L ~ i L P ~ i L i 4 (7) (7) 9
dz L ~ i i (7) 5 ( ) () : 51 511 ( ) () t i v it v i;t+1 = v it + a i + b 1i ~x 1 + b i ~x + 111+ i (8) ~x j = j a i = i b ji = j i i = 10
1 : ( : %) ( 1) ( ) 3 ( 3) i i t 0 1nt 1 3 4 5 D 1 863 17 00 0 00 08 19 864 10 04 03 09 3 00 4 849 90 10 08 4 00 00 43 869 77 10 5 00 00 06 05 780 09 D 00 00 00 00 00 1000 3: x x N(0; 6) (9) 6 x i i v i N( i ; i ) (10) i = v it + a i (11) i = b0 6b + Var( i ) (1) x i 51 v i;t+1 i i, i v 3 i = v i 0 i i (13) v 3 i 3 4% 3 849% 4 90% 5 10% 08% x v 3 i c c+1 x c;c+1 x Z xc01;c 1 p c = p e 0 1 z dz (14) x c;c+1 p c c 11
(1 + r)p 1 rp rp 3 t 3 5 850% D 08% 10% 4 90% 4% 03 0 01 0 1 3 x 45 = 0:09 x 5D = 0:41 x 34 = 01:4 x 3 = 1:73 v 3 i rp 1 P t 3 5: 4: v 3 i 5 PV def ( 5 ) PV def = d01 X t=1 D t rp + D d P (15) d = D t = t ( ) r = P = = PV nodef PV nodef = TX t=1 D t rp + D T P (16) T 1
0 0 40 60 80 100 (%) 6: 7: L L = PV nodef 0 PV def (17) 53 10,000 ( ) 6 ( 99%) 7 x y 4 x y 4 8 p L L = (a + bq(p)) 4 + (18) a, b q(p) p p = Z q(p) 01 1 p e 0 1 z dz (19) 13
^05-4 - 0 4 0 0 40 60 80 100 (%) 8: 4 9: 54 RAROC ( ) ( ) ( ) 14
^05-4 - 0 4 10: 4 10% 9 4 ( 10) 55 CreditMetrics JP Morgan 1997 4 CreditMetrics [6] CreditMetrics 1 1 CreditMetrics CreditMetrics 1 1 1 [0, 5] 15
6 [1] Altman ES Why business fail The Journal of Business Strategy, pp 15{1, 1983 [] Robert CMerton On the pricing of corporate debt: the risk structure of interest rates Journal of Political Economy, pp 449{470, 1973 [3] Fischer Black and Myron Scholes The pricing of options and corporate liablities Journal of Political Economy, pp 637{654, 1973 [4] TR Fleming and DP Harrington Counting process and survival analysis John Wiley and Sons, 1991 [5] JP Morgan Risk Metrics Technical Document JP Morgan, 199 [6] JP Morgan Credit Metrics Technical Document JP Morgan, 1997 [7] JD Kalbeish and RL Prentice The Statistical Analysis of Failure Time Data John Wiley and Sons, 1980 [8] M Kijima and K Komoribayashi A markov chain model for valuing credit risk derivatives preprint, 1997 [9] Moody's Investors Service,, 1, 1994 [10] Platt HD and Platt MB Business cycle eects on state corporate failure rates Journal of Economics and Business, pp 113{ 17, 1994 [11] Robert AJarrow, David Lando, and Stuart MTurnbull A markov model for the term structure of credit risk spreads Review of Financial Studies, pp 481{53, 1997 [1], pp 7{100, 1994 16
[13], (), 1997 [14],, 7 1996 [15] I, 1994 [16] II, 1994 [17], pp 40{57, 7 1996 [18], pp 5{54, 1997 [19],, 6 1996 [0], JCR, pp 5{9, 1996 [1] ALM, 1995 [],, 1997 [3] 4, 6 1996 [4],, pp 10{, 11 1995 [5], 1997 [6], 1997 17