1 (Basel Committee on Banking Supervision, BCBS) (BCBS(24), BCBS(215) ) *1 ( ) ( (1997) (213a,b) ) 2 *1 (214) 1
() ( ) ( ) (1996) (1997) (1997) EaR (Earning at Risk) VaR 2 1 1 ( ) ( ) Memmel (214) () 2 (214) 2
(1997) (1997) 2 2 3 4 2 (1996) (1997) Memmel (214) (214) ( 1) ( 2) ( 1) :, : ( 2) (PSJ ) 2 2.1 3
将来キャッシュフロー推計 1 24 1 214 9 1 銀行 B/S 構成依存関係( コピュラ) 市場金利モデル Nelson-Siegel モデル 信用リスクモデル Credit Metrics 金利追随率モデル 1ファクターモデルプリペイメントモデル リスク評価経済環境シナリオの生成資産負債シナリオ生成 CF 生成 リスク評価 預入 貸出資産モデル GBM PSJモデル固定性預金比モデル 上武 枇々木モデルロールオーバーモデル 定率 1 2.2 3 Nelson-Siegel (Diebold and Li (26)) t τ y t (τ) (1) ( ) ( ) 1 e λτ 1 e λτ y t (τ) = β 1,t + β 2,t + β 3,t e λτ (1) λτ λτ β 1 β 2 β 3 λ β 3 3 (2) AR(1) β k,t = c k + φβ k,t 1 + ε k,t (k = 1, 2, 3) (2) J.P.Morgan (1997) (Credit Metrics TM ) Credit Metrics TM 214 6 3 ( t ) 2.3 (211) () 4
( ρ t = T D t /LD t ) t ρ t r t ρ t = (α 1 ln r t α 2 )t + α 3 ln r t + α 4 (3) 1 PSJ (Prepayment Standard Japan) 6 6 6 % m CPR m (4) CPR m (%) = min (6m/6, x) (4) 2.4 CVaR CVaR := E[RT Net] R f T CVaR[R Net T ] + E[RNet T ] (5) E[x] x RT Net T ( ) R f T T CVaR 99% 1 3 3.1 B/S 1 = 1 (6) B/S 3 (6 ) *2 (6 ) = ( + + ) + (7) 2 1 1/3 1 *2 3 5
3 3 3 B/S ( ) 1 26.36 6 15. 5 15.44 6 58.11 3 15.63 1 35. 3 15.63 1 136.58 6 61.57 9.79 6 61.57 216.96 5 2.25 83.5 5 2.25 5 96. 5 96. 1 85.15 74.1 42.92 677.86 677.86 2.2, 2.3 AR(1) 4 5 4 AR(1) c φ σ ϵ R 2 β 1.69.96.121.911 β 2.62.946.167.893 β 3.238.918.329.871 5 AAA AA A BBB BB B CCC AAA 91.% 9.% 764 AA.8% 93.9% 5.2%.1% 3,228 A 1.8% 94.3% 3.7%.1%.1% 7,53 BBB 3.8% 93.4% 2.7%.1% 7,274 BB.3% 7.9% 86.6% 2.6% 2.6% 798 B.8% 9.9% 77.% 12.3% 131 CCC 4.5% 95.5% 44 6
*3 6 7 6 Σ β 1 β 2 β 3 ( ) ( ) β 1 1 β 2.86 1 β 3.24.7 1 ( ).43.45.3 1 ( ).3.34.2.91 1 7 a b σ e R 2 6 1.365%.716.63%.855 6 6.12%.445.27%.924 1 1.12%.589.43%.895 6.17%.36.23%.891 3.2 4 (2) (4) (1) (2) 4 1. (3 ) 2. (1 ) 3. ( ) 4. ( ) (3) (4) ( ) 3 *3 2 Russell/Nomura Russell/Nomura () Large Small 7
3.3 (1) 2 ( ) 2 1 ( B/S ) ( B/S ) 2 ( ) ( ) ( ) 2 1% (1 ) 3 3 1% ( ) 3 ( ) ( ) 1% 8
( ) B/S ( ) 2 B/S ( ) 4 5 4 5 ( ) 3.4 (2) 3 %.5%.1% CVaR 6 7 修正期間収益調整 CVaR レシオ 1.9.8.7.6.2.15.1.5 経済価値.5 -.5.1.2.3.4.5 金利上昇率 (%) 修正期間収益 経済価値調整 CVaR レシオ 期待修正期間収益 ( 兆円 ) 7 6 5 4 3 2 1 1 2 3 4 5 6 期間 変化なし.1% 上昇.2% 上昇.3% 上昇.4% 上昇.5% 上昇 6 CVaR 7 7 7 9
CVaR *4.5% 8 8.5% 8.2 8.4 7.53 7.7 99%VaR 5.92 6.23 5.67 6.7 8 99%Volume at Risk (VaR) 6 2 B/S 5 ALM 3.5 (3) 8 9.5% CVaR 1 CVaR ( ) *4 M LD t X t M LD = X tt LD 1
8 8 期待修正期間収益 ( 兆円 ) 7 6 5 4 3 2 1 追随率 % 追随率 2% 追随率 4% 追随率 6% 追随率 8% 追随率 1% 1 2 3 4 5 6 期待修正期間収益 ( 兆円 ) 7 6 5 4 3 2 1 追随率 % 追随率 2% 追随率 4% 追随率 6% 追随率 8% 追随率 1% 1 2 3 4 5 6 期間 期間 8 9 調整 CVaR レシオ 1.2 1.8.6.4.2 貸出追随率預金追随率.2.4.6.8 1 追随率 1 CVaR 修正期間収益調整 CVaR レシオ.7.6 -.1.5 -.2.4 -.3.3 -.4.2 修正期間収益 -.5.1 経済価値 -.6 -.7.1.2.3.4.5 金利上昇率 (%) 11 CVaR 経済価値調整 CVaR レシオ 3.6 (4) ( (214)) ( ) 1.25 CVaR 11
4 [1] Basel Committee on Banking Supervision (24) Principles for the Management and Supervision of Interest Rate Risk (http://www.bis.org/publ/bcbs18.pdf) [2] Basel Committee on Banking Supervision (215) Interest rate risk in the banking book - Consultative Document (http://www.bis.org/bcbs/publ/d319.pdf) [3] Diebold, F.X. and C. Li (26), Forecasting the Term Structure of Government Bond Yields, Journal of Econometrics, Vol.13, pp.337-364 [4] Memmel,C.(214), Banks interest rate risk: the net interest income perspective versus the market value perspective, Quantitative Finance, Vol.14, No.6, pp.159-168 [5] (211),, (), pp.196-223, [6] (1996), -VaR -, 15 4, pp.23-59. [7] (214) (http://www.fsa.go.jp/common/law/guide/city.pdf) [8] (25),, 24 2, pp.115-162 [9] (213a)- - (https://www.boj.or.jp/announcements/release 213/data/rel131118a1.pdf) [1] (213b) - - (https://www.boj.or.jp/announcements/release 213/data/rel131118a2.pdf) [11] (214), 214, pp. 34-35 [12] (1997) EaR VaR - -,, 16 3, pp.61-8 12