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1 Abstract JP Morgan CreditMetrics (1) () (3) (4)

2 1 BIS BIS 1 BIS 1 3 ALM (1) Value at Risk () (3) RAROC (Risk Ajusted Return On Capital) (4)

3 % (= p ) ~x X Prf~x Xg = p p p 99% 1% [4] 3 3

4 100 A 100 A [18] 4 () 4 (1) () (3) (4) RiskMetrics [5] 41 ( ) 4

5 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

6 1: Aaa Aa A Baa Ba B [9] 3 3 (1) 3 4 t n n + 1 X n n + 1 h n = Prfn X n + 1g () X 6

7 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

8 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 0 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

9 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

10 dz L ~ i i (7) 5 ( ) () : ( ) () t i v it v i;t+1 = v it + a i + b 1i ~x 1 + b i ~x i (8) ~x j = j a i = i b ji = j i i = 10

11 1 : ( : %) ( 1) ( ) 3 ( 3) i i t 0 1nt D D : 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

12 (1 + r)p 1 rp rp 3 t % D 08% 10% 4 90% 4% 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

13 (%) 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

14 ^ (%) 8: 4 9: 54 RAROC ( ) ( ) ( ) 14

15 ^ : 4 10% 9 4 ( 10) 55 CreditMetrics JP Morgan CreditMetrics [6] CreditMetrics 1 1 CreditMetrics CreditMetrics [0, 5] 15

16 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,

17 [13], (), 1997 [14],, [15] I, 1994 [16] II, 1994 [17], pp 40{57, [18], pp 5{54, 1997 [19],, [0], JCR, pp 5{9, 1996 [1] ALM, 1995 [],, 1997 [3] 4, [4],, pp 10{, [5], 1997 [6],

IMES DISCUSSION PAPER SERIES Discussion Paper No. 99-J- 9 -J-19 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN

IMES DISCUSSION PAPER SERIES Discussion Paper No. 99-J- 9 -J-19 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN 100-8630 03 IMES Discussion Paper Series 99-J- 9 -J-19 1999 6 * * [1999] *(E-mail: