CDO 2010 5 18 CDO(Collateralized Debt Obligation) Duffie and Garleânu[4] CDO CDS(Credit Default Swap) Duffie and Garleânu[4] 4 CDO CDS CDO CDS CDO 2007 CDO CDO CDS 1 1.1 2007 2008 9 15 ( ) CDO CDO 80 E-mail:taiji.ohka@gmail.com E-mail:stk25616a@ae.keio.ac.jp 1
BIS CDO CDO CDO CDO Cifuentes and O Connor[1] Finger[6] Li[8] Duffie and Garleânu[4] CDO Merton[9] CDO 1 CDO CDO CDS CDO three jump model Longstaff and Rajan[10] CDS CDS CDO Duffie and Garleânu[4] CDO CDS(Credit Default Swap) CDS CDS CDS CDS CDS CDS CDO CDS ISDA(the International Swaps and Derivatives Association) CDS 2007 62.2 CDS 1 2
CDS CDS CDS George[7] CDS CDS CDS Duffie and Singleton[3] RMV(recorvery of market value) RMV CDS RMV CDS CDS 4 CDS CDO CDO (2006 9 20 2007 12 10 ) (2007 12 10 2009 12 9 ) CDO CDO 2 3 George [7] CDS CDO 2 3 4 2 CDO 2.1 CDS 2.2 3 3
2.4 2.5 2.1 CDS CDS CDS CDS λ L CDS L L CDS Duffie and Singleton[4] RMV RMV T τ ϕ(τ) ϕ(τ) = (1 L)v(τ, T ), λ L CDS CDS George[7] 2 CDS ( ) ( ) CDS r x t(x > t) R(t, x) R(t, x) = x t rdu, t CDS t = 0 t CDS S(t) CDS T (T > 0) 1 1 t = 0 T CDS S(0) CDS S(0) 3 τ(τ < T ) τ R A R A = E Q t [ = S(t)E Q t S(t) ] m exp( R(t, t i ))I {τ>ti } i=1 [ m ] exp( R(t, t i ))I {τ>ti }, (1) 2 CDS 3 n S(t) CDS i=1 4
1: CDS (1) E Q t t Q τ R(t, t i ) t i t I {τ>tj } { 1 (τ > t i ) I {τ>ti } = 0 (τ t i ) τ > 0 Y (τ) ϕ(τ) 1 Y (τ) = 1 ϕ(τ), Duffie, Pan, and Singleton[2] 1 T t v(t, T ) T v(t, T ) = exp( R(t, T )) Pr[τ > T t] + (1 L) t exp( R(t, u))f (t, u)du, (2) (2) T 1 f (t, x) t x Pr Q [τ < x t] f (t, x) = d dx Pr [τ > x t] Q t R B t T R B = E Q t [ ] exp( R(t, τ))y (τ)i{τ tj,t j + t}. (3) 5
CDS (1) (3) (4) S(t) = EQ t = T t R A = R B, (4) [ exp( R(t, τ))y (τ)i{tj + t>τ>t j }] Q [ ], m exp( R(t, t j ))I {τ>tj } j=1 exp( R(t, x)) {1 (1 L)v(x, T )} f (t, x)dx m, (5) exp( R(t, t j ) Pr Q [τ > t j t] j=1 2.2 Duffie and Garleânu[4] CDS t t t t + t λ λ Pr[τ < t + t t] = λ t. (6) (6) t λ t Pr[τ < t + t t] t t t + t t λ(t) t < τ t + x ( t+x )] Pr[τ < t + x t] = E t [exp λ(u)du, x > 0, t E t t t s λ(t) dλ(t) = κ(θ λ(t))dt + σ λ(t)dw (t) + J(t), (7) W (t) J(t) J(t) µ l κ, θ, σ, µ, l 6
κ, θ, σ, µ, l κ θ σ µ l Duffie and Kan[5] t x E Q t (8) [ ( t+x )] exp λ u du = e α(x)+β(x)λ(t), (8) t f (t, x) = d dx Pr[τ > x t] = exp {α(x t) + β(x t)λ(t)} [α (x t) + β (x t)λ(t), ] (9) α(x) β(x) α (x) β (x) α(x) = κθ( c 1 d 1 ) β(x) = b 1 c 1 d 1 1 eb 1 x c 1 +d 1, e b 1 x α (x) = κθβ(x) + l ln c 1+d 1 e b 1x c 1 +d 1 µβ(x) 1 µβ(x), β (x) = κβ(x) + 1 2 σ2 β 2 (x) 1, b 1 = κ 2 + 2σ 2, c 1 = κ+ κ 2 +2σ 2 2, d 1 = κ κ 2 +2σ 2 2, a 2 = d1 c 1, b 2 = b 1, c 2 = 1 µ c 1, d 2 = d 1+µ c 1, + κθ c 1 x + l(a 2c 2 d 2 ) b 2 c 2 d 2 ln c 2+d 2 e b2x c 2 +d 2 + ( l c 2 ) l x, Duffie and Garleânu[4] 1 X κ, θ X, σ, µ, l X Y κ, θ Y, σ, µ, l Y X Y X + Y κ, θ, σ, µ, l θ = θ X + θ Y l = l X + l Y 1 2.3 1 X C(i,j) X C(i) X C X G X C(i,j) (κ, θ XC(i,j), σ, µ, l XC(i,j) ) X C (i) (κ, θ XC(i), σ, µ, l XC (i)) X C (κ, θ XC, σ, µ, l XC ) X G (κ, θ XG, σ, µ, l XG ) X C(i,j) X C(i) X C X G (i = 1, 2,, n, j = 1, 2,, m, C = 1, 2,, l ) λ C(i,j) = X C(i,j) + X C(i) + X C + X G (κ, θ C(i,j), σ, µ, l C(i,j) ) 7
X C(i,j) X C(i) X C X G 4 1 2 3 4 4 X C(i,j) X C(i) X C X G X C(i,j) C i j 1 X C(i) C i 2 X C C 3 X G 4 ρ C(i,j) = l X G, l C(i,j) (10) ρ C(i,j) = l X C, l C(i,j) (11) ρ C(i,j) = l X C(i) l C(i,j), (12) ρ C(i,j) = l X C(i,j) l C(i,j), (13) E Q t (10) (13) 4 4 4 t t + s(s > 0) [ ( t+x )] exp λ C(i,j) (u)du = exp[α(x) + β XC(i,j) (x)x C(i,j) (t) + β XC(i) (x)x C(i) (t) + β XC (x)x C (t) + β XG (x)x G (t)], t α(x) = α XC(i,j) (x) + α XC(i) (x) + α XC (x) + α XG (x). f (t, x) = exp { α(x t) + β C(i,j) (x t)c i,j (t) + β C(i) (x t)x C(i) (t) + β C (x t)x C (t) + β G (x t)x G (t) } [ ] α (x t) + β C(i,j) (x t)x i,j(t) + β C(i) (x t)x C(i)(t) + β C(x t)x C (t) + β G(x t)x G (t), α (x) = α C(i,j) (x) + α C(i) (x) + α C(x) + α G(x), 8
2.4 [13] CDO t(t = 0, 1,, N) F S (t) F M (t) F E (t) C S C M t L(t) t Loss S (t) Loss M (t) Loss E (t) (i, j) CDO CDS S i,j (i = 1, 2,, m.j = 1, 2,, n) r (i, j) τ i,j (τ i,j > 0) t + 1 CDO spr(t + 1) m n spr(t + 1) = S i,j I {τi,j >t} + (e r 1)(F S (t) + F M (t) + F E (t)) (F S (t)c S + F M (t)c M ), i=1 j=1 Loss E (t+1) Loss E (t + 1) = min {F E (t) + spr(t + 1), L(t + 1)}, t + 1 F E (t + 1) = F E (t) + spr(t + 1) Loss E (t + 1), Loss M (t + 1) = min {F M (t), max {0, L(t + 1) F E (t) spr(t + 1)}}, t+1 F M (t + 1) = F M (t) Loss M (t + 1), 9
Loss S (t + 1) = min {F S (t), max {0, L(t + 1) F E (t) F M (t) spr(t + 1)}}, t + 1 F S (t + 1) = F S (t) Loss S (t + 1), 2.5 CDO CDO CDO (7) i, j λ i,j 4 λ C(i,j) (t) = X C(i,j) + X C (i) + X C + X G, (14) X C(i,j) (t) = X C(i,j) (t t) + κ(θ XC(i,j) X C(i,j) (t t)) t + σ X C(i,j) (t t)ε XC(i,j) t + JXC(i,j) (t), X C(i) (t) = X C(i) (t t) + κ(θ XC(i) X C(i) (t t)) t + σ X C(i) (t t)ε XC(i) t + JXC(i) (t), X C (t) = X C (t t) + κ(θ C X C (t t)) t + σ X C (t t)ε C t + JC (t). X G (t) = X G (t t) + κ(θ G X G (t t)) t + σ X G (t t)ε G t + JG (t). (15) ε XC(i,j) ε XC(i) ε C ε G N(0, 1) J XC(i,j) J XC(i) J C J G J k (t) = { m k l k t 0 1 l k t. m k µ (k = X C(i,j), X C(i), C, G) (15) (14) C(i, j) t t + t (15) CDO 4 4 2 X C(i,j), X C(i) 2 10
3 CDO 3.1 3.2 3.3 2 3.1 CDS CDO 1 4 Quick 19 72 CDS CDS CDS 3 CDS Quick 2006 9 20 2009 12 9 3 5 r 1 L Rating and Investment Information, Inc [12] L = 0.95 CDS T 1 360 T = 1800 2 5 R I A ( 5405) R I AA Rating and Investment Information,Inc [12] 0.07 0.2 R I 72 2 2 2006 9 20 2009 12 9 2006 9 20 2007 12 9 2007 12 10 2009 12 9 3 2007 CDS 2 2006 9 20 2009 12 9 CDS 2 2006 9 20 2007 CDS 2009 CDS 3 CDS 2006 9 20 2007 12 9 2007 12 10 2009 12 9 2006 9 20 2009 12 9 3 3 B 5 1 2 11
2: 2006 9 20 2009 12 9 CDS ( :bbs) 1 1 1 t p [0, p] Nelsen[11] Li[8] CDO 2.4 1 MATLAB CDO 1 10 0.1 20 0,2 70 0,7 4 1.5 L 95 r 1 CDO 72 CDS 2009 12 9 CDO 5 CDO 3.2 (15) CDO 12
(10) ρ C(i,j) ρ C(i,j) (11) 3 CDS (2006 9 20 2007 12 9 ) CDS (2007 12 10 2009 12 9 ) 3 4 5 72 (11) (12) (13) 3 ρ C(i,j) ρ C(i,j) 3 ρ C(i,j) ρ C(i,j) 19 1000 JAL 2010 1 19 ρ C(i,j) ρ C(i,j) 4 ρ C (i, j) 4 ρ C (i, j) 3 ρ C(i,j) ρ C (i, j) 5 5 ρ C(i,j) ρ C(i,j) 4 ANA ρ C(i,j) ρ C(i,j) JAL ρ 13
3: 14
4: 15
5: 16
3.3 CDO CDO CDO (2006 9 20 2009 12 9 ) (2007 12 10 2009 12 9 ) (2006 9 20 2007 12 9 ) CDS 2 1: (2007/12/10 2009/12/9) 100 99.88 0.40 99.89 68.60 21.22 CCC 10.09 0.36 1.46 B (2006/9/20 2009/12/9) 100.00 99.84 1.35 98.92 50.28 21.81 CCC 1.71 0.04 0.46 BB 2, (2007/12/10 2009/12/9) 100.00 97.20 8.57 84.40 19.16 16.03 CCC 0.00 0.00 0.00 AAA 0.00 0.00 0.00 0.00 0.00 0.00 AAA 0.00 0.00 0.00 AAA 1 (2007/12/10 2009/12/9) (2006/9/20 2009/12/9) 2 ( ), R I CDO 1 99.88 99.84 10 17
6: 6 6 10 10 10 1 68.60 50.28 20 6 BBB 0.36 0.04 1 1 6 6 7 8 70 30 7 8 30 2 1 18
7: (2006 9 20 2009 12 9 ) 8: (2007 12 10 2009 12 9 ) 19
10 9 9: 2 (2007 12 10 2009 12 9 ) 2 9 2 2 10 2 10 2 3.96 4.71 2 13.55 3.63 10 2 CDO 11 5 30 50 80 11 20
10: 2 (2007 12 10 2009 12 9 ) 11: (2007 12 10 2009 12 9 ) 21
8 40 40 20 40 12 12: ( 40 20 40 ) 2: ( 40 20 40 ) (2007/12/10 2009/12/9) 100.00 56.91 12.48 0.03 0.00 0.07 AA 0.00 0.00 0.00 AAA 12 2 12 22
AAA 4 CDS CDO CDO 4 4 4 CDO CDO CDO CDO [1] Cifuentes,A. and G. O Connor. The Bionomial Expanision Method Applied to CBO/CLO Analysis. Moody sinvestors Service, 1996. [2] Duffie, D., J. Pan, and K. Singleton. Transform Analysis and Asset Pricing for Affine Jump Diffusion. Econometrica, Vol.12, pp.1343-73, 2000. [3] Duffie, D. and K. Singleton. Modeling term Structures of Defaultable Bonds. Review of Financial Studies, 1999. [4] Duffie, D., N. Garleânu.Risk and Valuation of Collateralized Debt Obligations. Financial Analysts Journal, January-February, pp.41-59, 2001. [5] Duffie, D., R. Kan. A Yield Factor Model of Interest Rates.Mathematical Finance, Vol.6, pp.379-406, 1996. 23
[6] Finger, C. C.A Comparison of Stochastic Default Rate Models. Working Paper, The RiskMetrics Group, 2000. [7] George Chacko, Anders Sjoman, Hideto Motohashi, Vincent Dessain. Credit Derivative: A Primer on Credit Risk, Modeling, and Instruments,Wharton School Publishing, 2006.(,,,,,,2008.) [8] Li, D. X. On Default Correlation:A Copula Approach. The Journal of Fixed Income, Vol.9, pp.43-54, 2000. [9] R, C, Merton. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance, Vol.29, pp.449-470, 1974. [10] Longstaff,Francis A. Arivind Rajan. An Empirical Analysis of the Pricing of Collateralized Debt Obligations. Journal of Finance,2007. [11] Nelsen, R. B. An Introduction to Copulas, Springer, New York, 1999. [12] Rating and Investment Information, Inc. R I Tranche Pad Version 1.0 Technical Document.R I, 2007. [13],. -ABS CDO., 2009 3 5. A 3: (2009 6 19 : : http : //www.r i.co.jp/jpn/news t opics/detail/200906/j09 a 066a.pdf) 1 2 3 4 5 6 7 8 9 10 AAA 0.00 0.00 0.00 0.00 0.00 0.15 0.29 0.29 0.29 0.29 AA 0.00 0.00 0.00 0.00 0.05 0.10 0.16 0.33 0.52 0.71 A 0.07 0.17 0.28 0.43 0.58 0.73 0.98 1.27 1.53 1.78 BBB 0.09 0.30 0.52 0.75 1.06 1.36 1.66 1.88 2.19 2.48 BB 1.95 3.38 4.95 6.09 6.92 7.89 9.30 10.80 11.99 13.15 B 8.70 14.04 18.46 20.47 23.09 24.71 27.05 28.28 29.56 30.88 4: 72 (R I 2009 12 31 : ) AAA AA A BBB B 1 24 37 9 1 24
5: R I 72 (2009 12 31 ) A A BBB A A AA A AA A AA A A AA A A A A A AA A NEC A A A A AA A AA A AA NTT AA BBB KDDI A A NTT A AA A AA A JR AA JT A BBB AA BBB AA BBB AA AA A A A AAA A BBB A A A BBB AA A BBB AA ANA BBB JFE AA JAL CCC AA A A A AA A A A 25
B 6: (r = 0.01 L = 0.95 T = 1800) :2006 9 20 2009 12 9 σ µ κ l C θ C RSME 4.560E-06 1.081E-05 4.560E-06 1.081E-05 1.081E-05 1.236E-04 7: (r = 0.01 L = 0.95 T = 1800) :2006 9 20 2009 12 9 θ C(i) l C(i) 4.700E-05 4.700E-05 2.723E-05 2.723E-05 2.943E-05 2.943E-05 2.739E-05 2.739E-05 1.297E-05 1.297E-05 2.911E-05 2.911E-05 2.699E-05 2.699E-05 3.183E-05 3.183E-05 1.395E-05 1.395E-05 2.979E-05 2.979E-05 1.371E-05 1.371E-05 2.687E-05 2.687E-05 3.026E-05 3.026E-05 6.498E-05 6.498E-05 1.163E-05 1.163E-05 1.324E-05 1.324E-05 1.229E-05 1.229E-05 2.709E-05 2.709E-05 2.874E-05 2.874E-05 26
8: (r = 0.01 L = 0.95 T = 1800) :2006 9 20 2009 12 9 l C(i,j) θ C(i,j) 1.755E-06 1.755E-06 2.604E-06 2.604E-06 2.207E-06 2.207E-06 2.468E-06 2.468E-06 2.238E-06 2.238E-06 JT 2.593E-06 2.593E-06 2.168E-06 2.168E-06 1.767E-06 1.767E-06 2.386E-06 2.386E-06 1.942E-06 1.942E-06 1.844E-06 1.844E-06 2.056E-06 2.056E-06 1.917E-06 1.917E-06 2.014E-06 2.014E-06 1.823E-06 1.823E-06 1.849E-06 1.849E-06 2.517E-06 2.517E-06 1.921E-06 1.921E-06 2.707E-06 2.707E-06 1.939E-06 1.939E-06 2.640E-06 2.640E-06 2.060E-06 2.060E-06 2.436E-06 2.436E-06 2.290E-06 2.290E-06 1.903E-06 1.903E-06 1.824E-06 1.824E-06 1.927E-06 1.927E-06 2.642E-06 2.642E-06 2.141E-06 2.141E-06 1.898E-06 1.898E-06 1.905E-06 1.905E-06 2.087E-06 2.087E-06 2.555E-06 2.555E-06 1.857E-06 1.857E-06 3.210E-06 3.210E-06 7.768E-06 7.768E-06 2.458E-06 2.458E-06 4.426E-06 4.426E-06 NEC 2.716E-06 2.716E-06 4.203E-06 4.203E-06 2.548E-06 2.548E-06 5.572E-06 5.572E-06 2.443E-06 2.443E-06 1.843E-06 1.843E-06 2.505E-06 2.505E-06 1.789E-06 1.789E-06 2.533E-06 2.533E-06 3.021E-06 3.021E-06 2.994E-06 2.994E-06 4.118E-06 4.118E-06 2.499E-06 2.499E-06 JFE 4.185E-06 4.185E-06 2.426E-06 2.426E-06 4.583E-06 4.583E-06 2.444E-06 2.444E-06 4.913E-06 4.913E-06 2.525E-06 2.525E-06 ANA 1.514E-06 1.514E-06 2.500E-06 2.500E-06 JAL 1.449E-05 1.449E-05 2.751E-06 2.751E-06 6.283E-06 6.283E-06 1.970E-06 1.970E-06 6.332E-06 6.332E-06 2.067E-06 2.067E-06 6.974E-06 6.974E-06 NTT 2.506E-06 2.506E-06 7.441E-06 7.441E-06 KDDI 2.591E-06 2.591E-06 4.255E-06 4.255E-06 NTT 2.505E-06 2.505E-06 4.718E-06 4.718E-06 27
9: (r = 0.01 L = 0.95 T = 1800) 2006 9 20 2007 12 9 σ µ κ l C θ C RSME 0.000002 3.304E-06 2.000E-06 3.304E-06 3.304E-06 5.999E-5 10: (r = 0.01 L = 0.95 T = 1800) 2006 9 20 2007 12 9 θ C(i) l C(i) 1.450E-05 1.450E-05 1.334E-05 1.334E-05 1.358E-05 1.358E-05 1.298E-05 1.298E-05 1.289E-05 1.289E-05 1.319E-05 1.319E-05 1.314E-05 1.314E-05 1.320E-05 1.320E-05 1.340E-05 1.340E-05 1.341E-05 1.341E-05 1.314E-05 1.314E-05 1.319E-05 1.319E-05 1.350E-05 1.350E-05 2.068E-05 2.068E-05 1.283E-05 1.283E-05 1.294E-05 1.294E-05 1.291E-05 1.291E-05 1.295E-05 1.295E-05 1.366E-05 1.366E-05 28
11: (r = 0.01 L = 0.95 T = 1800) 2006 9 20 2007 12 9 l C(i,j) θ C(i,j) 9.290E-06 9.290E-06 8.555E-06 8.555E-06 9.330E-06 9.330E-06 8.511E-06 8.511E-06 8.956E-06 8.956E-06 JT 8.727E-06 8.727E-06 9.119E-06 9.119E-06 8.290E-06 8.290E-06 9.354E-06 9.354E-06 8.958E-06 8.958E-06 8.627E-06 8.627E-06 8.991E-06 8.991E-06 8.694E-06 8.694E-06 8.920E-06 8.920E-06 8.543E-06 8.543E-06 8.408E-06 8.408E-06 8.546E-06 8.546E-06 8.600E-06 8.600E-06 8.700E-06 8.700E-06 8.641E-06 8.641E-06 8.585E-06 8.585E-06 8.643E-06 8.643E-06 8.534E-06 8.534E-06 8.858E-06 8.858E-06 8.617E-06 8.617E-06 8.357E-06 8.357E-06 8.623E-06 8.623E-06 9.110E-06 9.110E-06 8.914E-06 8.914E-06 8.586E-06 8.586E-06 8.617E-06 8.617E-06 8.828E-06 8.828E-06 8.638E-06 8.638E-06 8.555E-06 8.555E-06 8.968E-06 8.968E-06 8.876E-06 8.876E-06 8.491E-06 8.491E-06 8.634E-06 8.634E-06 NEC 8.872E-06 8.872E-06 8.615E-06 8.615E-06 8.717E-06 8.717E-06 8.730E-06 8.730E-06 8.344E-06 8.344E-06 8.545E-06 8.545E-06 8.417E-06 8.417E-06 8.432E-06 8.432E-06 8.648E-06 8.648E-06 9.427E-06 9.427E-06 1.160E-05 1.160E-05 8.665E-06 8.665E-06 8.518E-06 8.518E-06 JFE 8.689E-06 8.689E-06 8.334E-06 8.334E-06 8.743E-06 8.743E-06 8.399E-06 8.399E-06 8.745E-06 8.745E-06 8.732E-06 8.732E-06 ANA 7.420E-06 7.420E-06 8.637E-06 8.637E-06 JAL 1.607E-05 1.607E-05 8.708E-06 8.708E-06 8.557E-06 8.557E-06 8.660E-06 8.660E-06 8.550E-06 8.550E-06 9.010E-06 9.010E-06 8.639E-06 8.639E-06 NTT 8.520E-06 8.520E-06 8.703E-06 8.703E-06 KDDI 8.660E-06 8.660E-06 8.528E-06 8.528E-06 NTT 8.510E-06 8.510E-06 8.707E-06 8.707E-06 29
12: (r = 0.01 L = 0.95 T = 1800) 2007 12 10 2009 12 9 σ µ κ l C θ C RSME 9.999E-06 1.793E-05 9.999E-06 1.793E-05 1.793E-05 1.094E-04 13: (r = 0.01 L = 0.95 T = 1800) 2007 12 10 2009 12 9 θ C(i) l C(i) 4.367E-05 4.367E-05 1.102E-05 1.102E-05 1.329E-05 1.329E-05 1.136E-05 1.136E-05 9.920E-06 9.920E-06 1.314E-05 1.314E-05 1.087E-05 1.087E-05 1.644E-05 1.644E-05 1.050E-05 1.050E-05 1.381E-05 1.381E-05 1.042E-05 1.042E-05 1.072E-05 1.072E-05 1.430E-05 1.430E-05 5.791E-05 5.791E-05 8.847E-06 8.847E-06 1.012E-05 1.012E-05 9.353E-06 9.353E-06 1.106E-05 1.106E-05 9.880E-06 9.880E-06 30
14: (r = 0.01 L = 0.95 T = 1800) 2007 12 10 2009 12 9 l C(i,j) θ C(i,j) 3.328E-05 3.305E-05 1.866E-05 2.208E-05 5.388E-05 5.321E-05 1.000E-05 1.000E-05 5.514E-05 5.444E-05 JT 1.702E-05 1.980E-05 3.738E-05 4.655E-05 1.000E-05 1.000E-05 4.169E-05 5.464E-05 2.611E-05 3.255E-05 2.359E-05 2.550E-05 2.317E-05 2.853E-05 2.952E-05 3.335E-05 2.087E-05 2.529E-05 2.115E-05 2.256E-05 1.129E-05 1.181E-05 1.204E-05 1.286E-05 1.629E-05 1.886E-05 1.666E-05 1.933E-05 1.736E-05 2.036E-05 1.523E-05 1.733E-05 2.472E-05 3.073E-05 1.000E-05 1.000E-05 3.673E-05 4.537E-05 1.412E-05 1.579E-05 2.407E-05 2.609E-05 1.571E-05 1.803E-05 4.069E-05 5.281E-05 2.774E-05 3.494E-05 2.785E-05 3.101E-05 1.429E-05 1.603E-05 3.326E-05 3.923E-05 2.534E-05 2.769E-05 2.568E-05 2.812E-05 3.786E-05 4.772E-05 4.442E-05 5.786E-05 1.866E-05 1.965E-05 3.246E-05 3.728E-05 NEC 3.051E-05 3.489E-05 3.081E-05 3.482E-05 2.465E-05 2.682E-05 3.788E-05 4.631E-05 1.809E-05 1.899E-05 2.570E-05 2.813E-05 2.322E-05 2.504E-05 2.186E-05 2.339E-05 2.405E-05 2.606E-05 4.445E-05 5.865E-05 3.207E-05 3.737E-05 1.414E-05 1.582E-05 2.226E-05 2.388E-05 JFE 1.483E-05 1.679E-05 1.598E-05 1.660E-05 1.893E-05 2.255E-05 1.776E-05 1.861E-05 2.216E-05 2.708E-05 1.409E-05 1.574E-05 ANA 6.980E-06 6.987E-06 1.336E-05 1.471E-05 JAL 7.642E-05 6.275E-05 2.208E-05 2.695E-05 1.232E-05 1.326E-05 3.313E-05 3.882E-05 1.271E-05 1.380E-05 3.575E-05 4.333E-05 1.700E-05 1.981E-05 NTT 8.070E-06 8.070E-06 1.988E-05 2.385E-05 KDDI 2.174E-05 2.174E-05 1.642E-05 1.903E-05 NTT 8.072E-06 8.072E-06 2.073E-05 2.510E-05 31
15: 2 (r = 0.01 L = 0.95 T = 1800) 2007 12 10 2009 12 9 sigma mu kappa l2 theta2 RSME 1.200.E-05 3.750.E-05 1.200.E-05 3.750.E-05 3.750.E-05 1.185.E-04 1.000.E-05 1.940.E-05 1.000.E-05 1.940.E-05 1.940.E-05 1.118.E-04 1.000.E-05 1.070.E-05 1.000.E-05 1.070.E-05 1.070.E-05 1.411.E-04 1.000.E-05 1.340.E-05 1.000.E-05 1.340.E-05 1.340.E-05 1.356.E-04 1.000.E-05 1.240.E-05 1.000.E-05 1.240.E-05 1.240.E-05 1.376.E-04 1.000.E-05 1.210.E-05 1.000.E-05 1.210.E-05 1.210.E-05 1.380.E-04 1.000.E-05 2.160.E-05 1.000.E-05 2.160.E-05 2.160.E-05 1.018.E-04 1.820.E-05 1.000.E-05 1.820.E-05 1.000.E-05 1.000.E-05 1.449.E-04 1.320.E-05 1.000.E-05 1.320.E-05 1.000.E-05 1.000.E-05 1.436.E-04 1.000.E-05 1.060.E-05 1.000.E-05 1.060.E-05 1.060.E-05 1.409.E-04 1.000.E-05 1.380.E-05 1.000.E-05 1.380.E-05 1.380.E-05 1.340.E-04 1.000.E-05 1.470.E-05 1.000.E-05 1.470.E-05 1.470.E-05 1.333.E-04 1.000.E-05 1.910.E-05 1.000.E-05 1.910.E-05 1.910.E-05 1.097.E-04 9.998.E-06 2.587.E-05 9.998.E-06 2.587.E-05 2.587.E-05 1.041.E-04 9.999.E-06 2.057.E-05 9.999.E-06 2.057.E-05 2.057.E-05 1.090.E-04 1.000.E-05 1.301.E-05 1.000.E-05 1.301.E-05 1.301.E-05 1.363.E-04 1.181.E-05 4.447.E-05 1.181.E-05 4.448.E-05 4.449.E-05 1.515.E-04 1.000.E-05 1.128.E-05 1.000.E-05 1.128.E-05 1.128.E-05 1.397.E-04 1.000.E-05 1.394.E-05 1.000.E-05 1.394.E-05 1.394.E-05 1.347.E-04 32
16: 2 (r = 0.01 L = 0.95 T = 1800) 2007 12 10 2009 12 9 l C(i,j) θ C(i,j) 2.331E-04 2.331E-04 1.215E-05 1.215E-05 1.281E-04 1.281E-04 1.052E-05 1.052E-05 1.249E-04 1.249E-04 JT 1.202E-05 1.202E-05 4.961E-06 4.961E-06 1.015E-05 1.015E-05 7.161E-06 7.161E-06 1.366E-05 1.366E-05 2.282E-06 2.282E-06 1.245E-05 1.245E-05 2.806E-06 2.806E-06 1.184E-05 1.184E-05 2.145E-06 2.145E-06 9.455E-06 9.455E-06 1.106E-05 1.106E-05 1.016E-05 1.016E-05 1.295E-05 1.295E-05 1.040E-05 1.040E-05 1.229E-05 1.229E-05 1.205E-05 1.205E-05 1.025E-05 1.025E-05 4.716E-06 4.716E-06 1.028E-05 1.028E-05 2.288E-06 2.288E-06 1.064E-05 1.064E-05 6.669E-06 6.669E-06 1.384E-05 1.384E-05 2.641E-06 2.641E-06 1.032E-05 1.032E-05 3.610E-06 3.610E-06 1.118E-05 1.118E-05 2.443E-06 2.443E-06 1.682E-05 1.682E-05 3.992E-06 3.992E-06 1.030E-05 1.030E-05 1.707E-06 1.707E-06 NEC 1.262E-05 1.262E-05 1.574E-06 1.574E-06 1.112E-05 1.112E-05 2.435E-06 2.435E-06 1.017E-05 1.017E-05 2.143E-06 2.143E-06 1.073E-05 1.073E-05 1.931E-06 1.931E-06 1.098E-05 1.098E-05 7.541E-06 7.541E-06 1.503E-05 1.503E-05 1.049E-05 1.049E-05 1.067E-05 1.067E-05 JFE 1.066E-05 1.066E-05 1.001E-05 1.001E-05 1.166E-05 1.166E-05 1.017E-05 1.017E-05 1.247E-05 1.247E-05 1.088E-05 1.088E-05 ANA 6.131E-07 6.131E-07 1.065E-05 1.065E-05 JAL 6.986E-06 6.986E-06 1.292E-05 1.292E-05 1.069E-05 1.069E-05 2.738E-06 2.738E-06 1.078E-05 1.078E-05 3.396E-06 3.396E-06 1.194E-05 1.194E-05 NTT 1.057E-05 1.057E-05 1.278E-05 1.278E-05 KDDI 1.170E-05 1.170E-05 1.048E-05 1.048E-05 NTT 1.056E-05 1.056E-05 1.155E-05 1.155E-05 33