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    beto27's Avatar
    beto27 Posts: 3, Reputation: 1
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    #1

    Sep 5, 2009, 03:12 AM
    Bond Pricing
    Hi I need some help with this question:

    Assume that the current one-year spot rate is 8% and that the forward rates for one year hence and two years hence, are, respectively:

    f(1,2) = 9%
    f(2,3) = 10%

    What should the market price of an 8% coupon bond, with a $1000 face value, maturing three years from today be? The first interest payment is due one year from today. Interest is payable annually.

    Hope someone can help.
    Thanks!
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #2

    Sep 5, 2009, 05:02 AM
    Discount each cash flow with the rates applicable to each one-year interval. As an example, the last CF would be priced at



    Obviously, for the first CF you need only the spot rate, and for the second you'll use both the spot and the (1, 2) forward.
    morgaine300's Avatar
    morgaine300 Posts: 6,561, Reputation: 276
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    #3

    Sep 5, 2009, 06:22 PM

    What is a "spot rate"? Do they mean the coupon rate?
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #4

    Sep 6, 2009, 06:30 AM
    The spot is the rate which applies immediately. E.g. a 1-year spot would be the interest rate that applies to the period beginning today and ending one year from today.

    A forward is the rate which applies over the stated interval; e.g. the (2, 3) forward is the rate which applies to the one-year interval beginning two years from today (the parenthetical notation "bookends" the applicable time period).

    Forward rates are available from banks via a mechanism called a forward rate agreement (FRA). Since these rates (just like the spots) are set by the market, it's more accurate to price long-dated cash flows (such as a bond) using the appropriate forward rates.

    Have a great holiday weekend!
    beto27's Avatar
    beto27 Posts: 3, Reputation: 1
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    #5

    Sep 10, 2009, 07:47 AM
    Thank you ArcSine for your help.

    So the final answer would be:

    80/1.08 + 80/(1.08)(1.09) + 1080/(1.08)(1.09)(1.10) = $976.06 ?

    Thanks just let me know if that is right.
    ArcSine's Avatar
    ArcSine Posts: 969, Reputation: 106
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    #6

    Sep 10, 2009, 08:14 AM
    You got it... good job.
    beto27's Avatar
    beto27 Posts: 3, Reputation: 1
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    #7

    Sep 11, 2009, 04:14 AM
    Cool thanks!
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