24Lecture24

# Bonds with oating rate coupons have a duration of

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Unformatted text preview: appens when the coupon is a fraction of a ﬂoating rate? When anything has an exact value there is a story! Fixed Income II: R. J. Hawkins Econ 136: Financial Economics 14/ 19 So what about that zero duration? Let’s look inside that price equation: P= 1 1+r 1+r = 1+r zero-coupon bond + r , 1+r annuity or Pﬂoater = PZCB + Pannuity Consequently, the duration of the ﬂoater Dﬂoater is: Dﬂoater = DZCB + Dannuity Fixed Income II: R. J. Hawkins Econ 136: Financial Economics 16/ 19 Dﬂoater = DZCB + Dannuity Let’s calculate the component durations: Dannuity = − DZCB = − = d 1 dr 1 + r 1 , (1 + r )2 d dr r 1+r 1 r + , (1 + r ) (1 + r )2 1+r r =− + , 2 (1 + r ) (1 + r )2 1+r −r =− , (1 + r )2 1 =− (1 + r )2 =− DZCB = −Dannuity ∴ Dﬂoater ≡ DZCB + Dannuity = 0 Fixed Income II: R. J. Hawkins , Econ 136: Financial Economics 17/ 19 Swap Valuation: An Example Given the following term-structure of par coupons . . . Year 1 2 3 4 5 6 Interest Rates (%) Par Spot Forward 8.75 8.75 8.75 9.00 9.01 9.27 9.28 9....
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## This note was uploaded on 01/23/2014 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at Berkeley.

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