IMES DISCUSSION PAPER SERIES Discussion Paper No J INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN

Size: px

Start display at page:

Download "IMES DISCUSSION PAPER SERIES Discussion Paper No J INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN"

ありあいなおか
5 years ago
Views:

1 IMES DISCUSSION PAPER SERIES Dscusso Paper No. 00-J-0 0 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN

3 IMES Dscusso Paper Seres 00-J- -J-0 00 GMM O/N LIBOR HJM LIBOR GMMHJM JEL classfcato: G * E-mal: toshao.yoshba@boj.or.jp akra.eda@boj.or.jp

4 .. GMM O/N 4 LIBOR HJM 6. 6 GMM 8

5 . market prce of rsk stataeous spot rate LIBOR BGM Brace Gatarek ad Musela [997] [999]

6 Geeralzed Method of Momets GMM O/N HJM 4 Heath Jarrow ad Morto [99] HJ Nelso ad Segel [987]. GMM α β γ W d ( α + β ) dt + γ dw () GMM Hase [98] GMM Ogak [99] 4 HJM

7 γ 0 γ 0. 5 α 0 γ 0 α 0 5 O/N O/N LIBOR 9 () t+ t ( α + β t ) t + ε t. () ε N(0 t γ t t) () E[ ε t ] 0 (4) E [ ε t t ] 0 (5) E[ ε t γ t t] 0 (6) 5 Cha Karoly Logstaff ad Saders [99] 6 O/N 7 () () 8 O/N 9

8 E[( ε t γ t t) t ] 0 (7) α β γ Geeralzed Method of Momets GMM TSP 0 O/N O/N O/N α β γ (.0060) (-.08) (.4565) (0.5) () d α γ β dt + dw β (8) α β 0 GMM [000] O/N t 4

9 α % β O/N 5.6 γ γ 0 γ > 0 γ 0 γ 0 γ O/N α β γ (.455) (-.4748) ( ) (.68) γ 0.5 [995]Kogure [997]98 99 O/N γ γ O/N Hrak ad Takezawa [997] TIBOR γ 0.5 5

10 α β γ (.46) (-.885) (.64) (.07940) % O/N α β γ (.567) (-.5605) (0.5698) ( ) O/N 0.4 γ LIBOR O/N LIBOR 4 Bloomberg LIBOR (A-) 6

11 α β γ (-.408) ( ) (.6) (5.55) α β γ (.7580) (-.696) ( ) (.6477) 0.57 O/N LIBOR LIBOR 0.60γ.5 O/N β O/N 75.9LIBOR 8.95 () LIBOR 7

12 α β γ () 5. HJM s t t + dt s < t f() s t m m HJM m df ( s t) ( s t) dt + ( s t) db ( s) (9) B (s) o arbtrage codto m t ( s t) ( s t){ λ ( s) + ( s v) dv} (0) λ ()market s prce of rsk Rtchke ad Sakarasubramaa [995] s 5 8

13 6 κ ( Tt) ( tt) e ( tt ). () () 78 HJM LIBOR HJM LIBOR Nelso ad Segel [987] λ () s x f (x) x y f ( x ) f ( x) ax + b + c ( x ) () x + r c x 0 r 0 () ( x x ) + ( x x ) > x x 0 (4) 6 Heath Jarrow ad Morto [99] 7 8 9

14 x y f ( x ) LIBOR MM6MM YY4Y5Y7Y0Y 0Y 0.75Y.5Y.5Y.5Y4.5Y6Y8.5YY y LIBOR LIBOR MM6MM LIBOR f ( t t + / 65) r(x) x f (x) f ( x) r( x + x) ( x + x) r( x) x x (5) LIBOR f (x) r(x) r( x) x x 0 f ( y) dy (6) () 0

15 r 4 ( x) ax + b + c ( x x ) + 4x (7) D(x) r(x) LIBOR R(x) D(x) D( x) exp( r( x) x) (8) R( x) D( x) x (9) m p(m) ( ) p m m ( D( m)) D (0) y () + a b c () y f x ) ( (Y) 0 y f ( x ) x 0 f ( x ) 0 a + c ( x x ) + 0 () f (x) (7)(0)

16 LIBOR () + a b c f (x) M LIBOR YY4Y5Y7Y0Y 0.75Y.5Y.5Y.5Y4.5Y6Y8.5Y 0. LIBOR y f (x) Nelso ad Segel [987] f (x) β 0 β β τ f ( x) β 0 + β exp( x / τ ) + β [( x / τ )exp( x / τ )]. () r(x) (6) r( x) β 0 + ( β + β )[ exp( x / τ )]/( x / τ ) β exp( x / τ ) () LIBOR R(x) r(x) 65 r( x) l + R( x) x x 60. (4) ()(8)(0) β 0 β β τ

17 LIBOR (4) MM 6MM () YY4Y5Y7Y0Y (0) 9 β 0 β β τ f (x) HJM HJM k g( k) g( k) g( + k) g( k) HJM (9)() def κk ς ( k) Var[ g( k)] e t + t (5) ς ( k ) ςˆ ( k) [ g( k) g( k)] (6) g( k) g( k) (7) k 0MM6MYYY4Y5Y7Y9Y ˆ ς ( k) (6) t / 65 κ L κ ) ( κk L( κ ) [ ˆ ς ( k) e ] k (8) 9 ()(8)(0)

18 ˆ ς ( k) ˆ ς ( k) (8) HJM κ 6.E E-0.E κ.4e-0 -.0E-0.6E κ 6.5E E- 7.55E-8 4

19 κ 0 ˆ ς ( k) ς ( k) ˆ ς ( k) ˆ (8) HJM 0 0 κ Myazak ad Yoshda [998] HJM κ κ.87e-4 9.8E- 7.6E-5 κ 0 Myazak ad Yoshda [998] 5 5

20 κ.e-7 -.6E E- κ HJM κ κ 0 Myazak ad Yoshda [998] LIBOR. κ κ κ 0 κ 6

21 GMM O/N LIBOR HJM LIBOR 7

22 8 GMM ] [ E ) ( r g θ (A-) j j j ˆ ) ˆ ˆ ˆ ( ˆ r g θ (A-) ) ( N ˆ ˆ ˆ ˆ ˆ (A-) ) ( θ 0 ] [ E (A-4) 0 ] [ E (A-5) 0 ] [ ] ) [( E E (A-6) (A-4)(A-6) 0 ]) [ ( ]) [ ( ]) [ ( + + E E E (A-7) ) ( ) ( ) ( + + (A-8)

23 Geeralzed Method of MometsGMM E[ g ( θ )] 0 E[ g ( θ )] 0 (A-9) E[ g ( θ )] 0 r r r G g ( θ ) g ( θ ) gr ( θ ) (A-0) D r r G DG GMM [996] A- mutar.xls O/N (A-) MUTANR 4 O / N _ rate MUTANR l (A-) Hase [98] D 4 TSP [995] 9

24 A- TSP READ(FILE'mutar.xls'); FRML EQ MUTANR(+)-MUTANR-(ALPHA+BETA*MUTANR)*/65; FRML EQ (MUTANR(+)-MUTANR-(ALPHA+BETA*MUTANR)*/65)**- (SIGMA*MUTANR**GAMMA)***/65; PARAM ALPHA 0.0 BETA.0 SIGMA 0. GAMMA 0.0; SMPL 945; GMM(INST(CMUTANR)) EQ EQ; 0

25 Brace A. D. Gatarek ad M. Musela The Market Model of Iterest Rate Dyamcs Mathematcal Face 7() 997 pp Cha K. C. G. A. Karoly F. A. Logstaff ad A. B. Saders A Emprcal Comparso of Alteratve Models of the Short-Term Iterest Rate The Joural of Face 47() July 99 pp Hase L. P. Large Sample Propertes of Geeralzed Method of Momets Estmators Ecoometrca pp Heath D. R. A. Jarrow ad A. Morto Bod Prcg ad the Term Structure of Iterest Rates: A New Methodology for Cotget Clam Valuato Ecoometrca 60() 99 pp Hrak T. ad N. Takezawa How sestve s short-term Japaese terest rate volatlty to the level of the terest rate? Ecoomcs Letters 56 November 997 pp. 5-. Kogure A. A New Approach to the Estmato of Stochastc Dfferetal Equatos wth a Applcato to the Japaese Iterest Rates IMES Dscusso Paper 97-E-8 Bak of Japa 997. Myazak K. ad T. Yoshda Valuato Model of Yeld-Spread Optos the HJM Framework The Joural of Facal Egeerg 7() 998 pp Nelso C. ad A. Segel Parsmoous Modelg of Yeld Curves Joural of Busess 60(4) 987 pp Ogak M. Geeralzed Method of Momets: Ecoometrc Applcatos Hadbook of Statstcs Vol.: Ecoometrcs edted by G.S. Maddala C.R.Rao ad H.D. Vod North-Hollad Amsterdam 99 pp Rtchke P. ad L. Sakarasubramaa A Multfactor Model of the Qualty Opto Treasury Futures Cotracts The Joural of Facal Research 8() 995 pp Vascek O. A. ad H. G. Fog Term Structure Estmato Usg Expoetal Sples The Joural of Face 7() 98 pp

26 000. : BGM 99-J TSP 995.

第一次大戦後の日本における国債流通市場の制度改革

第一次大戦後の日本における国債流通市場の制度改革 IMES DISCUSSION PAPER SERIES Discussion Paper No. 2009-J-23 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN 103-8660 2-1-1 http://www.imes.boj.or.jp IMES Discussion Paper Series 2009-J-23 2009