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Math Help - Interest rate swap problem

  1. #1
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    Interest rate swap problem

    An interest rate swap is based on the yield curve given below.

    s_{1}=0.03
    s_{2}=0.04
    s_{3}= x
    s_{4}=0.05

    The fixed payment swap rate is R=0.4936. Find the 3-year spot rate x.

    I'm having trouble solving for x. For some reason I keep getting a negative number. This is what I've been doing.

    R=0.4936=\frac{1-\frac{1}{1.05^{4}}}{\frac{1}{1.03}+\frac{1}{1.04^{  2}}+\frac{1}{(1+x)^{3}}+\frac{1}{1.05^4}}

    => \frac{0.177297525}{2.7772586888+\frac{1}{(1+x)^{3}  }}=0.4936

    0.177297525=0.492401092+\frac{0.4936}{(1+x)^{3}}

    From there


    \frac{1}{(1+x)^{3}}=-2.418065972



    Which isn't correct. The book shows

    \frac{1}{(1+x)^{3}}=0.87379


    Can someone point my mistake out please? Thanks
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  2. #2
    MHF Contributor
    Joined
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    Re: Interest rate swap problem

    You should use use .04936 as swap rate (kick yourself!).

    Also, your 2.77725.... is not quite right: I get 2.71813...
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