II III II 1 III ( ) [2] [3] [1] 1 1:

2015 4 16 1. II III II 1 III () [2] [3] 2013 11 18 [1] 1 1:

[5] [6] () [7] [1] [1] 1998 4 2008 8 2014 8 6 [1] [1] 2 3 4 5 2. 2.1. t Dt L DF t A t (2.1) A t = Dt L + Dt F (2.1) 3 2 1 2008 9 2008 8 2008 9 2 2008 8 3 4 QQ Shapiro-Wilk 3 p 0.5649 3() QQ p 1.09 10 5 4() QQ 1 1 R ecompose 2 1 µ 3 Shapiro-Wilk 2

h Œ µ µ Ø Ø f { Ø Ø Ø 2: 3: QQ 3

4: QQ A t λ t (2.3) ( ) At+1 λ t = ln (2.2) A t λ t = µt + σz (2.3) () λ t 1 [1] 1: µ σ µ σ 1998 4 2008 8 [1] 0.002396 0.001625 0.000497 0.010060 1998 4 2014 8 0.002304 0.002134 0.001042 0.019927 µ σ µ 2 λ t (DW) DW 2.819(p : 1 : 778 10 8 ) DW 2.199(p : 0.09962) p 0.1% p 10% [1] p p 10% λ t 4

2.2. 2.2.1. () 5 l l l l e e Œ>/KZ el el l l e e Œ >/KZ el el l l l l l l 5: 1 LIBOR 1% 2008 9 2010 1 4 6 3 4 e e e e eee e ee e e e e e eee e e ee e e e 6: 5 0.84 1 2 3 4 5

3 2.2.2. (2.4) ρ t = DF t D L t (2.4) D L t t DF t t 7 e e e eee e ee e eee e ee e 7: 6 0.925 0.938 8 [1] 2006 2008 9 e e e Œ >/KZ l l el el l l Œ >/KZ l l el el l l l l l l 8: 6

[1] [4] (2 ) ( 9) l 9: µpµµ µµ µµµ µ µ µ µµ µ xœµ µµµ µµ µµµµ µµ µµµ µµµµ oµµµ µ µµ 1990 2013 5 1 LIBOR 10 4 6 0.8209 10: 4 6 5 7

4 3 4 1 2 r t ln r t 5 2.2.3. 1 : ρ t = α 1 (r t α 2 )t + α 3 (2.5) 2 : ρ t = α 1 (r t α 2 )t + α 3 r t + α 4 (2.6) 3 : ρ t = (α 1 ln r t α 2 )t + α 3 (2.7) 4 : ρ t = (α 1 ln r t α 2 )t + α 3 ln r t + α 4 (2.8) (2002 4 ) 2002 4 2014 8 1 4 2 2: 1 α 1 ( 10 3 ) α 2 ( 10 3 ) α 3 ( 10 2 ) α 4 ( 10 2 ) α 1 ( 10 3 ) α 2 α 3 α 4 0.803-66.771 39.596-1.198-2.264 1.330 1 0.818-58.575 39.607-0.966-2.826 1.328 2 0.828-51.272 39.624-0.754-3.640 1.326 3 0.869-38.500 39.621-0.540-5.120 1.325 6 0.980-5.217 39.638 0.042 67.302 1.321 1 1.140 46.402 39.766 1.075 2.783 1.317 2 α 1 ( 10 3 ) α 2 ( 10 3 ) α 3 ( 10 2 ) α 4 ( 10 2 ) α 1 ( 10 3 ) α 2 ( 10 2 ) α 3 α 4 5.627 57.385-32.943 41.639 18.560 22.925-1.349 1.414 1 4.753 55.132-27.240 41.317 18.363 23.151-1.338 1.412 2 4.003 52.164-22.271 41.026 18.392 23.164-1.343 1.411 3 3.528 50.383-18.893 40.813 18.429 23.176-1.348 1.410 6 2.628 48.327-12.167 40.409 18.159 23.571-1.337 1.406 1 0.722 26.231 3.326 39.550 14.374 28.334-1.058 1.386 3 α 1 ( 10 3 ) α 2 ( 10 3 ) α 3 ( 10 2 ) α 4 ( 10 2 ) α 1 ( 10 3 ) α 2 ( 10 2 ) α 3 α 4 0.292-0.778 39.752-0.139 0.313 1.323 1 0.302-0.788 39.801-0.082 0.300 1.322 2 0.310-0.795 39.856-0.026 0.288 1.322 3 0.321-0.808 39.911 0.030 0.276 1.321 6 0.349-0.833 40.105 0.188 0.244 1.321 1 0.378-0.827 40.532 0.473 0.195 1.325 4 α 1 ( 10 3 ) α 2 ( 10 3 ) α 3 ( 10 2 ) α 4 ( 10 2 ) α 1 ( 10 3 ) α 2 ( 10 2 ) α 3 α 4 1.308-3.458-6.293 21.307 3.806-0.727-0.244 0.607 1 1.173-3.074-5.454 23.901 3.719-0.697-0.238 0.629 2 1.076-2.798-4.844 25.772 3.827-0.720-0.244 0.613 3 0.992-2.559-4.290 27.465 3.920-0.739-0.249 0.600 6 0.831-2.080-3.181 30.930 4.132-0.777-0.261 0.569 1 0.210-0.394 1.202 43.950 3.289-0.527-0.201 0.755 : *** 0.1%, ** 1%, * 5% 5 1 2 1 α 1 (r t α 2 )t = (α 1 ln r t α 2)t, α 2 = α 1 α 2 α 2 p α 2 α 2 = α 2/α 1 [1] 8

[1] 6 (2002 4 2008 9 ) 2 1 2 3 6 1 6 [1] 1 α 2 2 4 1 2 4 0.1% 24 1 0.1% 4 α 1 α 3 [1] α 3 6 2 1114 µµ Œ l µµ Œ l 11: ( 1) µµ Œ l µµ Œ l 12: ( 2) 9

µµ Œ l µµ Œ l 13: ( 3) µµ Œ l µµ Œ l 14: ( 4) [1] 0.010.04 2 4 1 3 4 2005 2008 9 [1] 1 3 2 1 4 15 4 [1] 4 0.055 10

µ } µ } µµ µµ 15: [1] 0.02 2.53 [1] 2 4 [1] 3. 3.1. 4 [1] 3 0.1% 50,000 1 (2.3) (3.1) λ t (2.2) (3.2) A t+1 ε t λ t = λ t 1 + λ t, λ t = µ t + σε t t (3.1) A t+1 = A t e λ t (3.2) 2 (3.4) Hull-White ρ t r t = (θ t ar t )t + σz t (3.3) ρ t = (α 1 ln r t α 2 )t + α 3 ln r t + α 4 + σ e e t (3.4) σ e e t 11

ε t e t Hull-White a = 0.0004, σ = 0.000192 3 A t ρ t D L t = A t 1 + ρ t (3.5) 4 E(D L t ) 99% Volume at Risk VaR(D L t ) a. X e 0 = D L 0 E(D L 1 ) X e t = E(D L t ) E(D L t+1), (t = 1,..., T 1) X e T = E(D L T ) b. Volume at Risk(VaR) X v 0 = D L 0 VaR(D L 1 ) X v t = VaR(D L t ) VaR(D L t+1), (t = 1,..., T 1) X v T = VaR(D L T ) Hull-White θ t 16() 2 A : 2014 8 B : 2014 2 e Ø Ø e e e e e 16: A 16 6 ln(r t )t α 1 ln(r t ) α 3 α 1 < α 3 t 6 B A A 12

α 3 ln r t (α 1 t α 3 ) ln r t t α 1 t 3.2. A B 17 17: 10 α 1, α 3 B A B 3.3. 1821 10 10 ( ) 17 10 B 10 97.0 60.4 18: (, A) 13

140.5 101.3 19: (, A) 93.0 57.9 20: (, B) 132.1 96.3 21: (, B) 14

3.4. () X t (3.6) T z L = T Xt z t t=1 D0 L (z {e, v}) (3.6) e v VaR 1 2 3 VaR 3 3: () A VaR VaR VaR 8.613 6.204 7.792 5.884 7.876 6.078 1 8.812 6.312 7.892 5.876 8.005 6.117 2 8.965 6.385 7.830 5.833 8.036 6.129 3 9.086 6.470 7.779 5.801 8.062 6.139 B VaR VaR VaR 8.127 5.891 7.063 5.477 7.223 5.686 1 8.355 6.021 7.163 5.481 7.358 5.736 2 8.712 6.200 7.101 5.440 7.393 5.751 3 8.881 6.313 7.050 5.406 7.429 5.771 3 A VaR AA-Kijima [2] (1995 2010 ) AA-Kijima 4 AA-Kijima 4 AA-Kijima () β Y z 0 = X z 0 + T t=1 Y z t = (1 β)x z t 15 βx z t

4: AA-Kijima AA-Kijima(*1) µ 3 22.7% 9.5% 12.4% (2007) σ 4.9% 4.0% 4.1% 3.238 () 5.373 () 4.771 () 6.204 () 5.884 () 6.078 () (*2) 1 6.312 () 5.876 () 6.117 () (2011) 2 6.385 () 5.833 () 6.129 () 3 6.470 () 5.801 () 6.139 () (*1) 1995 2010 ( [2]) (*2) 2002 4 2014 8 (3.7) T T Xt z = Yt z = D0 L (z {e, v}) (3.7) t=0 t=0 T z C = T Yt z t=1 D0 L t = (1 β)t z L (z {e, v}) (3.8) 30%(β = 0.3) 5 5: (: 30%) () A VaR VaR VaR 6.029 4.343 5.454 4.119 5.514 4.254 1 6.169 4.418 5.524 4.113 5.603 4.282 2 6.276 4.470 5.481 4.083 5.625 4.290 3 6.360 4.529 5.445 4.061 5.643 4.297 B VaR VaR VaR 5.689 4.123 4.944 3.834 5.056 3.980 1 5.848 4.215 5.014 3.837 5.151 4.015 2 6.098 4.340 4.971 3.808 5.175 4.025 3 6.217 4.419 4.935 3.784 5.200 4.040 3 0.7 16

4. 2002 4 1 (2.8) 6 4 4 7 6: 2002 4 2014 8 2002 4 2008 9 2008 10 2014 8 2006 4 2008 9 [1] 7: 4 α 1 ( 10 3 ) α 2 ( 10 3 ) α 3 ( 10 2 ) α 4 ( 10 2 ) 1.308-3.458-6.293 21.307 1.279 1.945-3.986 31.745 0.098-1.267-3.213 52.525-1.267 1.868 7.897 29.870 α 1 ( 10 3 ) α 2 ( 10 2 ) α 3 α 4 3.806-0.727-0.244 0.607 3.506 0.210-0.162 0.963 1.061-0.276-0.143 1.304 0.600 0.306-0.043 0.863 : *** 0.1%, ** 1%, * 5% 7 α 1 α 3 2 α 1 α 3 α 1 α 3 0.1% 22 23 22 23 17

e e e e e e e e e e e 22: () e e e e e e e e e e e e e e e e e e e e e 23: () e e 18

5. [1] (2008 9 ) [1], :,, 2011 4, pp.196-223. [2] :, BOJ Reports & Research Papers, 2011 11 2014 3. http://www.boj.or.jp/research/brp/ron_2011/ata/ron111124a.pf [3], 2013 11 18. http://www.boj.or.jp/announcements/release_2013/rel131118a.htm [4],, http://www.shiruporuto.jp/finance/chosa/ [5],,,, 2012, pp. 227-238. [6],, SAS All Analytics 2014 http://www.boj.or.jp/research/brp/ron_2011/ata/ron111124a.pf [7],,,,,,,,, ( 9, pp.113-143), 2014 10,. 19