第9巻信用リスクモデル

第 9 巻信用リスクモデル信用リスクモデル森平爽一郎早稲田大学 0 1. 1. 2. 2. 3 1. PD) 2. RR)LGD=1-RR) 3. JPD)R) 3. 1. (VaRCTE) 2. 4. - 1 -

1 1. 1. 2. (Bankrupcy) 2. 3 1. PD) 2. RR),LGD=1-RR) 3. 3. 4. a. b. c. d. 2.1 () 1. RNVR) 2. CECerany Equvalen Mehod) ( 3. RADR: Rsk Adjused Dscoun Rae Mehod) - 2 -

2.2 PD (1) RR(1)= 1-LGD(1)) (C(1)) 1-PD (1) (C(1)) 0: :( 2.2 1(PD (1)) ECF1 PD 1 1LGD1 C1 1PD 1 C1 PD 1 1LGD 1 1PD 1 C 1 1 = 11(PD (1)) (1-PD (1)) - 3 -

2.2 1 ECF1 PD 1 1LGD1 C1 1PD 1 C1 1PD 1 1LGD 1 1 C 1 1PD 1 LGD 1 C 1 1 C 1 1 1 1 1 1 PD LGD 0,1 0,1 2.2 1C(1) 1((1)) B Z E CF 1,1 r 0 1 1 1 1 1 C 1 1r 0,1 1 0,1 C 1 r 0 1 Z 0,1 1-4 -

2.3 1 1C(1) () ()(PD P (1) 1r(0,1)s(0,1) B 0,1 P P 1 1 1 1 1 1 1 1 1r 0,11s 0,1 P 1 PD 1 LGD 1 P C 1 1 C 1 1r0,11s 0,1 1r0,11s 0,1 PD LGD C PD C P 1 C 1 1 s 0,1 1r 0,1 1 1 1 1 P 1 Z 0,1 2.4 2C(2) 2 12 1121 ECF2 1PD 1 PD 2 1LGD 2 C2 1PD 1 1PD 2 C2 1PD 1 1 PD 2 LGD 2 C 2 2 C 2 2 2 21PD 1 1PD 2LGD 2 2 ( 1 122 2-5 -

3.1 PD PD D N n 1 D PD n N =1,2,,n 1 () +1 (D )(N ) 3.2 (LPM: Lnear Probably Model) Y ( PD P ) ~ Y 1 0 1 X X X XX X X X X 0 50% 100% 150% 200% (DER ) - 6 -

3.3 ( PD P ) 1 X X X XX X X X X. 1. 2.() 0 50% 100% 150% 200% (DER ) 3.4 1. 2. 3. 4. =N(d 2 ) 5. N(d2)d 2-7 -

3.4 (=T) (A T ) E ~,0 A T = Max[Ã T D D T, 0] T T) rt F E0 e E 0 MaxA T DT,0 E = 0 er FT {E 0 [Max[Ã D T T,0]]} 2) 1) ( 34 A ~ T Pr (Ã A T TD DT T ) = N( N(d d2) 2 ) A 0 D T D 0 T(A T ) (D T ) =0 =T () 16-8 -

3.4 D T, E E S N 0 0 0 1)EE 0 =A A 0 N(d N d 1 )D 1 D T exp{r T rft N f T}N(d d 2 ) 2 [1n(A 2 [ln( A0 / D 0 /D T) T )+(r rf f A 2 A/2)T] 2 d 1 = 1 A A T T d 2 =d 1 A T 1) ( ) exp{ } ( ) d d T 2 1 A E E 0 2) A = 0 E AN 0 ( d1) E A 0 N(d 1 ) A 0 A r f PD Pr( A D ) 1 N( d ) T T 2 17. RR) 1. 100 2. 3. 1. RR 1. 2. 2. Workou RR P - 9 -

4.2 1. 1. ( 2. 2. 3. ( 4.2 CF R M C RR for 1, 2, L, T EAD EAD 0 0 EAD 0 = CF = R = M = C = = T = - 10 -

4.2 PV CF PV R M C RR for 1, 2, L, T EAD EAD 0 0 (=0)PV{}) EAD 1. ( 2. 3. 21 4.2 Franks, Servgny and Davydenko[2005] 22-11 -

4.3 1. 1. 1 2. U1 3. 2. 3. 5.1 1. 2. -1+1 3. 1. 1 2. 3. 4. 5. - 12 -

5.1 PD XY XY XY, PD PD PD XY, X Y 1 1 PD PD PD PD X X Y Y 1. JDP=PD XY PD X, PD Y 2. XX 1 3. (PD XY ()PD X PD Y XY 4. PD XY PD X PD Y XY 5. 5.2 T () D D TD TN - 13 -

5.2 () D D PD, D D 1 2 D D 1 N N 1 2 N N 1 PD, n 1 D D n 1 N N 1 1 =1,2,,n 27 5.2 DD N n n D =1 1 4 PD PD = = = 4 N =0.04=4% 4% 100 100 1 0.04 0.06 0.015 PD PD = 1 0.04+0.06+0.015 3.83% n n N N = =0.0383=3.83% 3 DPD D,j j 410 40 PD, j = D D j 410 N 0.0020 N = = 40 =0.0020 j 100200 20,000 N N j 100 200 20,000 n PD 1 D Dj 1, D = D [D 1] D 1 43 PD, j 0.0020 0.0055 0.0013 0.0029, N PD [N 1] = 43 =0.0012 PD,j = 1 DD 10099 n 0.0012 n 1 N 3 N 1 100 99 N N n j 1 = (0.0020+0.0055+0.0013)=0.0029 =1 NN j 3 j PD n, 1 = 1 D D D 1 1 PD, n n [D 1] =1 N [N 1] = 1 (0.0012+0.0032+0.0002)=0.0015 0.0012 3 0.0032 0.0002 0.0015 n 1 N 1 2 N - 14 -

5.3 (A )1 (A ) F A b F 1b F 2 1 F 1 A 5.3 1 A b F 1b 2 E F 0, E 0, Var F 1, Var 1, E F 0 d PD = Pr (Ã d ) PD PrA d JPD j = Pr (Ã d Ã j d j ) JPDj PrA d A j d j 30-15 -

A b F 1b 2 b ( F: E F 0, E 0, Var F 1, Var 1, E F 0 5.3 A j %, % % % Cov A A Asse bb, b Var A Var A 11 2,j %, % % % j Cov A A bb Var A Var A 11 Asse j j, j bb j - 16 -

6.1 PD ) LGDEAD PD() EAD=100) LGD=0.2) 0100 6.1 (EL)(UL) (EL) ULVaR - 17 -

6.2 1. F() 2. () 3. A 2 1 4. A d A% bf% b% 1. L LGD 2. L 0 5. ) 6. ))f(l) 7. EL)UL) 7 CRD) ( 1. 2. 3. 4. CDO () 36-18 -

7.1 CDS: Cred Defaul Swap A: B: B A B A( 7.12 II AB A B X Y - 19 -

7.2 TRS: Toal (Rae of)reurn Swap LIBOR 1. 2.(+) A: A B: (B) X 1. LIBOR+ 2. 7.3 ( CLN: Cred Lnked Noe 1. LIBOR+ 2. A:CLN B: ( CLN 1. LIBOR 2. - 20 -

第9巻 信用リスクモデル

第9巻信用リスクモデル