... FRA 13 30
... Forward Rate Agreement FRA 5.3 P.82
... FRA FRA T Long / Short Long: Fixed-rate payer 3 9 LIBOR 7.86
... FRA FRA r F (T T) = r (T t) r(t t) r F = r (T T) + r (T t) r(t t) T T = r +(r r) T t T T
... FRA FRA FRA FRA I t A T T FRA r F FRA r K t FRA FRA T [ Ae r F (T T) Ae r K(T T) ] e r (T t)
... FRA FRA FRA FRA II FRA FRA [ Ae r F (T T) Ae r K(T T) ] e r (T t) r K
... e International Money Market of the Chicago Mercantile Exchange (www.cme.com) e Sydney Futures Exchange e Toronto Futures Exchange e Montréal Stock Exchange e London International Financial Futures Exchange (www.liffe.com) e Tokyo International Financial Futures Exchange Le Marché à Terme International de France (www.matif.fr) Eurex (www.eurexchange.com)
... I
... II
... 3 3 3 3 CME
... 3
... 3
... 3 IMM Q = 100 (1 ) 10, 000 (100 0.25 (100 Q)) IMM 100
... 3 0.01% 1000000 0.0001 1 4 = 25 100 (1 3 LIBOR) = [100 (1 LIBOR) Q] 100 25 = ( LIBOR) 10000 25
... 3 Example 2007 9 17 EDU07 3 LIBOR 5.5975% EDU07 94.4025 2007 7 20 94.66 EDU07 (94.4025 94.66) 100 25 = 643.75
... 3 1 / /
... 15 15 100 000 CME
... 100 000 30 15 15 1 6 1 % 31.25 32 100 3 3 7:20-14:00 1 32 80-16 16 80 32 7 12:01
... / 1/32 100 80-16 80.5 80-16 1 000 80 16 = 80 500 32 = +
... 5.5 I 2007 10 3 2027 11 15 6.125% A 118.11 2007 5 15 2007 11 15
... 5.5 II 2007 5 15 2007 10 3 141 2007 5 15 2007 11 15 184 2007 10 3 100 6.125 2 141 184 = 2.347 118.11 + 2.347 = 120.457
... I 1 6% 15
... II 1 6% 1
... 5.5.1 I 2007 12 USZ7 5.5 A 2007 12 1 19 11 15 3 2007 12 1 19 9 2008 3 1
... 5.5.1 II 1 6% 2007 12 1 39 i=0 6.125% 2 1.03 i + 1 1.03 39 1 + ( 1.03 1) = 1.0295
... 5.5.1 III 3 2007 12 1.0295 6.125% 4 = 1.0142
... 100 = +
... 5.5.2 I 2007 10 3 USZ7 111.27 2007 12 3 A USZ7 1 000 (111.27 1.0142 + )
... 5.5.2 II 2007 12 3 2007 11 15 18 2007 11 15 2008 5 15 182 2007 12 3 A 100 6.125 2 18 182 = 0.303 A 1 000 (111.27 1.0142 + 0.303) = 113 153
... = + ( + ) = ( )
... 5.7 序 号 息 票 率 到 期 日 转 换 因 子 债 券 报 价 期 货 报 价 转 换 因 子 交 割 成 本 1 4.500 02/15/36 0.7978 96.91 88.77 8.14 2 4.750 02/15/37 0.8292 100.90 92.27 8.63 3 5.000 05/15/37 0.8628 104.91 96.00 8.91 4 5.250 11/15/28 0.9116 107.08 101.43 5.65 5 5.250 02/15/29 0.9111 107.05 101.38 5.67 6 5.375 02/15/31 0.9226 109.32 102.66 6.66 7 5.500 08/15/28 0.9415 110.25 104.76 5.49 8 6.000 02/15/26 1.0000 115.52 111.27 4.25 9 6.125 11/15/27 1.0142 118.11 112.85 5.26 10 6.125 08/15/29 1.0150 119.09 112.94 6.15 11 6.250 08/15/23 1.0250 117.09 114.05 3.04 12 6.250 05/15/30 1.0304 121.30 114.65 6.65 13 6.375 08/15/27 1.0428 121.09 116.03 5.06 14 6.500 11/15/26 1.0557 122.23 117.47 4.76 15 6.625 02/15/27 1.0703 123.92 119.09 4.83 16 6.750 08/15/26 1.0831 125.05 120.52 4.53 17 6.875 08/15/25 1.0940 125.76 121.73 4.03 18 7.125 02/15/23 1.1103 126.40 123.54 2.86 19 7.500 11/15/24 1.1570 132.61 128.74 3.87 20 7.625 02/15/25 1.1717 134.23 130.38 3.85
......1...2 F = (S I)e r(t t)...3...4
... 5.7 I 5.7 2007 10 3 USZ7 7.125% 2023 2 15 1.1103 126.40 2007 12 3 2 3.8% USZ7
... 5.7 II...1 5.15 2007 8 15 2008 2 15 100 7.125 2 49 184 = 0.949 5.15 126.40 + 0.949 = 127.349
... 5.7 III...2 2007 10 3 2007 12 3 I = 0...3 12 3 USZ7 61 0.1671 3.5 F = 127.349e 3.8% 0.1671 = 128.160
... 5.7 IV...4 5.16 2007 12 3 7.125 2 110 184 = 2.130 128.160 2.130 = 126.030...5 126.030 1.1103 = 113.510
......... LIBOR LIBOR
......... 2005 9 1 1 2.8% 3 LIBOR 3
......... 7 1
......... 7 1
......... I 4 4 = 2 + 3 1 2 6 3 7
......... II (I)
......... III (II) 4 = I VIII I FRA FRA
......... (I) FRA 4
......... (II)...1...2
......... V = B fl B fix V = B fix B fl B fix = n ke r it i + Ae r nt n i=1 B fl = (A + k )e r 1t 1
..... 7.1 I.... 3 LIBOR 4.8% 3 1 9 3 6 9 LIBOR 4.8% 5% 5.1%
..... 7.1 II.... k = 120 B fix = 120e 0.048 0.25 + 120e 0.05 0.5 + 10120e 0.051 0.75 = 9975.825 B fl = 10000 9975.825 10000 = 24.175 24.175
......... FRA FRA FRA (Ae r F(T T) Ae r K(T T) )e r (T t) FRA FRA
..... 7.2 I.... 3 LIBOR 4.8% 3 1 9 3 6 9 LIBOR 4.8% 5% 5.1% 3 4.8% 4 ln(1 + 4.8% 4 ) = 4.7714%
..... 7.2 II....
......... B fl = B fix
......... 7.3 I 2 3 LIBOR 3 3 1 3 6 9 12 15 18 21 2 4.8% 5% 5.1% 5.2% 5.15% 5.3% 5.3% 5.4% 3 4.8%
......... 7.3 II B fl = 10000 B fix = k 4 e 0.048 0.25 + k 4 e 0.05 0.5 + k 4 e 0.051 0.75 + k 4 e 0.052 1 + k 4 e 0.0515 1.25 + k 4 e 0.053 1.5 + k 4 e 0.053 1.75 + (10000 + k 4 )e 0.054 2 = 10000 k = 543 5.43% 3
......... 3 LIBOR
......... LIBOR LIBOR, LIBOR LIBOR LIBOR LIBOR Swap Spread the Term Structure of Swap Rate or the Swap Curve
.........
......... I LIBOR LIBOR r s e r 1 + r s e 2r 2 = r f1 e r 1 + r f12 e 2r 2 r s = e r 1 e 2r 2 e r 1 + e 2r 2 r f1 + e r 1 + e 2r 2 r f12
......... II 7 7 7
......... I Feldhütter and Lando 2008
......... II
......... LIBOR OIS I LIBOR OIS 3 LIBOR OIS 2007
......... LIBOR OIS II
谢 谢 http://e nance.org.cn zlzheng@xmu.edu.cn aronge@xmu.edu.cn