Lecture4-07

Lecture4-07 - ! " #$ % & & & ! " #$ (...

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Unformatted text preview: ! " #$ % & & & ! " #$ ( & & ! ' ! " #$ * * & & !# "# & !# "# $ ! 100eRT R T $ T ! 100e-RT % R ! ) ! " #$ * & Rc ' Rm' R c = m ln 1 + R m = m e Rc / m − 1 ( Rm m ) + ! " #$ (% ) T Maturity (years) 0.5 1.0 1.5 2.0 * $ T $ Zero Rate (% cont comp) 4.5 4.8 5.4 5.7 , ! " #$ / & % & $ &/ + . ' 0 ! , . ! " #$ / & $ 1 ! " #$ 0 & $ 0 1 2 ! " #$ 0 m A $ $ 1 P ! " ! " $ c= (100 − 100 P ) m A 3 ! " #$ Bond Principal (dollars) 100 100 100 100 100 Time to Maturity (years) 0.25 0.50 1.00 1.50 2.00 Annual Coupon (dollars) 0 0 0 8 12 Bond Cash Price (dollars) 97.5 94.9 90.0 96.0 101.6 ! " #$ %4 / (4 &( & 10 2 5 , %4 6 30 42 5 107 42 " 0 8 23 0 #12 . 0 ! " #$ %4 / & "2 0 $ ( 4 4e −0.10469×0.5 + 4e −0.10536×1.0 + 104e − R×1.5 = 96 R 9#" 8 " 0# &: , " 0- . #8 " ' ! " #$ 12 * 4 * Zero Rate (%) 11 10 10.469 10.127 10.536 10.681 10.808 9 0 0.5 1 1.5 2 2.5 Maturity (yrs) ) ! " #$ 5 % ; + ! " #$ * 5 Zero Rate for Year (n ) 1 2 3 4 5 (% per annum) 3.0 4.0 4.6 5.0 5.3 5.0 5.8 6.2 6.5 , Forward Rate (% per annum) an n -year Investment for n th Year ! " #$ 5 &: % R2 T1 T1 T2 T2 R1 0 & R2 T2 − R1 T1 T2 − T1 % $ & . ! " #$ 5 & T0 $ T R+T R &< T, ∂R ∂T ! " #$ 5 &( ) (* = 6! 2 ! " #$ 5 &( = ( $ 6! RK + &( = ( &< $ % 3 ! " #$ 7 &> &> & RF =( L =( + + L ( R K − R F )( T 2 − T1 ) e − R 2 T 2 T" RK T1 $ T1 R1 % L ( R F − R K )( T 2 − T1 ) e − R 2T 2 &< RK RM R1 ! " #$ 6 89 &( 8 . &? $ " & &< 1 $ 1 " 82 0. =( 4 . ! # ## # "# # =( ! " #$ && n i =1 $ ci ti ti cie B ) − yt i B & y * ∆B = −D∆y B ' ! " #$ * &< y m + ∆B = − & + BD∆y 1+ y m D 1+ y m @ A ) ! " #$ : &? <4 ; $ !! $ = $ " # 9 > B $0 &? , !# ## "# # & 60 ;5 , 5 1 3 ,# 0 64 84 0 4 !> 0 + ! " #$ * $+ n 9 c i t i2 e − yt i 1∂B C= = i =1 B ∂y 2 B so that ∆B 1 = − D∆y + C (∆y )2 B 2 2 , ! " #$ %4 & C+ + &D ' % : ' 4% & / + ' % . ...
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This note was uploaded on 12/14/2011 for the course FIN 5515 taught by Professor Staff during the Spring '10 term at FSU.

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