ALM

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1 ALM

2 ALM

3

4 4

5 ALM ALM [1] ALM [1] ALM 5

6 1 6

7 ALM ALMAsse and Liabiliy Managemen ALM 7

8 ALM 1-1 ALM 8

9 2 9

10 ( (

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12 / +1 3 [] 1 / [] 12

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15 15

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17 r1 : r% : S : B : : : I : : r Rr I 1 = r = Rr + I S = r +.5 = Rr + I +.6 B = r + = Rr + I Rr r 1 I 1 17

18 OPIX NomuraBPI

19

20 3-4 α : I β : I ε I : α : Rr β : Rr ε R r : I = α + β I + εi I I 1 Rr Rr (3.8) Rr = α + β Rr + εrr (3.9) Rr = r I (3.10) I = I 1 + ε I (3.11) Rr = R r + ε Rr (3.12)

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23 4 23

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27 /

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29 4.2.2 : a : a a a : : : Dr : α PVA : LS, a cou x, : a, a : : a : a : a : cin : a CIN : a SPVB : : a : F DE : : 29

30 (1) LS a, LS0, a2 1 + BUτ + BU a2 a τ = 1 = 1 LS0, a2 1, a ( ( 2 1 a a a2 1)) ( 1+ BU 0 ) a2 a 1 ( 1 ) ( 1 ),( 1 ) ( ) a a ( ) (2) cou = LS α, a, a 4.5 (4.) ( ) MNF =cou PVA a a a,a,a X, Dr X Dr (4) ( ) a2 a 1 1 C = MNF, a a a ( ) a, a, 1 2 a2 a1 1+ Dr (5) ( a a1 ) ( ) a2 a 1 NF = MNF, a a a ( ) a, a, 1 2 a2 a1 1+ Dr 4.8 a a 1 30

31 (6) a 1 2 (, τ, τ ) SNF = NF N τ = a (7) ( ) PVB = cou PVA, a a a a, a, a3 adr, (8) a 3 1 (, τ, τ ) SPVB = PVB N τ = a (9) d = SNF + SPVB ( ) DE = max d F, (10) a 2 1 (, τ, τ ) CIN = cin N τ = a (11) a 1 3 (, τ, τ ) COUT = cou N τ = a

32 BU I β = a a a a 0 a a a a

33 33

34 ALM 1 ALM

35 .2 ALM z j, yb ys vl j, j, () i 0 : j : j : j : (i) vl :0 : (i) W (i) (i) ρ () i j, () i 0 () i : i j :0 : i b :0 b :0 j j γ δ : CIN () i COUT CIN 0 COUT d : i () i () i : i : :0 : i Dr : Uv : Lv : UI : LI : UT : T : I : 35

36 0 z = b + yb ys j,0 j j,0 j,0 0 z j, = z j, 1 + ybj, ys j, ( = 1, T 1) -1 0 n ( 1 γ ) ρ ( 1 ) + yb + vl + COUT = b + γ ρ ys + CIN j,0 j, j,0 j,0 0 j= 1 j= 1 n j j 1 n () () () n i i i () i () i + γ ρ j,1 ybj,1 + vl1 + COUT1 = + r0 δ vl0 + γ ρ j,1 ys j,1 + CIN1 j= 1 j= 1 ( 1 ) ( 1 ) ( 1 ) j 0 j n () i () i () i () i () i () i () i ( 1+ γ ) ρ j, ybj, + vl + COUT = ( 1+ r 1 δ) vl 1 + ( 1 γ ) ρ j, ys j, + CIN ( = 2, T-1 j= 1 j= 1 n j j 1 () n i () i ( ) () i () i 1 = (1 γ) ρj,1 j, δ j= 1 W z r vl CIN COUT 36

37 1 1 ( δ) n () i () i () i () i () i () i γ ρ j, j, j= 1 W = (1 ) z r vl + CIN COUT ( = 2, T) vl Lv 0 0 Uv0 W 0 ρ j,0 z j,0 LI0 UI0 W0 0 vl Lv Uv ( = 1, W () i ρ j, z j,0 Lv Uv ( = 1, W ρ ( ) j,0 zj,0 b0 0 W 0 UT j () i ρ ( ) j z, j z, j, 1 W 0 UT ( = 1,, T 1) j 37

38 min 1 I I T i= 1 = 1 ( i ) q ω Dr s ubjec o W + q d ( i) ( i) ( i) ( i ) q 0 1 LPM ALM z j, yb ys j, j, 0 () i () i vl 0 vl d

39 39

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41 6.1 γ δ : Dr :0.05(5%) Uv:1 Lv :0 UI :0.5 LI :0 UT j :

42

43

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45 LPM b 0 : 900 b j :0 γ : δ: Dr :0.05 Uv:1 Lv :0 UT :0.5 j UI =

46

47 Risk Risk 0.5 Risk 47

48

49

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51 6.2.2 b 0 : 900 b j :0 γ : δ: Dr :0.05 Uv:1 Lv :0 U j :0.5 LI :0 j UT 1 = UT2 =

52 6-16 Risk 0.1 Risk

53 7 53

54 ALM / ALM 54

55 [1] ALM 2001 pp [2] 2002 pp81100 [3] 1999 pp3655 [4] 2001 [5] 2000 [5]J.Hull 2000 [6]

56 56

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6

O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-1 O1-2 O1-3 O1-4 O1-5 O1-6 O1-7 O1-8 O1-9 O1-10 O1-11 O1-12 O1-13 O1-14 O1-15 O1-16 O1-17 O1-18 O1-19 O1-20 O1-21 O1-22 O1-23 O1-24 O1-25 O1-26 O1-27 O1-28 O1-29 O1-30 O1-31 O1-32 O1-33 O1-34 O1-35

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