How to calculate one-year forward one-year rate?












1












$begingroup$


I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% respectively), how do we calculate the one-year forward one-year rate?



I just am confused as to which formula to use.






interest-rates finance statistics forward-rate







share|improve this question







New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 4




    $begingroup$
    (1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
    $endgroup$
    – Alex C
    7 hours ago
















1












$begingroup$


I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% respectively), how do we calculate the one-year forward one-year rate?



I just am confused as to which formula to use.






interest-rates finance statistics forward-rate







share|improve this question







New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 4




    $begingroup$
    (1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
    $endgroup$
    – Alex C
    7 hours ago














1












1








1





$begingroup$


I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% respectively), how do we calculate the one-year forward one-year rate?



I just am confused as to which formula to use.






interest-rates finance statistics forward-rate







share|improve this question







New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I'm just a little lost on how to calculate forward rates. I know this is an easy question, but, if we are given a one-year and two-year zero rate (let's say, for the sake of the argument, 2% and 3% respectively), how do we calculate the one-year forward one-year rate?



I just am confused as to which formula to use.






interest-rates finance statistics forward-rate




interest-rates finance statistics forward-rate






share|improve this question







New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question







New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question






New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 7 hours ago









Marie kMarie k

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91




New contributor




Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 4




    $begingroup$
    (1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
    $endgroup$
    – Alex C
    7 hours ago














  • 4




    $begingroup$
    (1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
    $endgroup$
    – Alex C
    7 hours ago








4




4




$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
7 hours ago




$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
7 hours ago










1 Answer
1






active

oldest

votes


















3












$begingroup$

Let ${r_t}_{t>0}$ be the spotrates and $f_{t,T}$ be the forward rate from time $t$ to $T$ for $t<T$. Then the general formula to compute $f_{t,T}$ is
$$
(1+r_T)^T=(1+r_t)^t(1+f_{t,T})^{T-t}
$$



Now you can solve for $f_{t,T}$ to obtain:



$f_{t,T}= left( frac{(1+r_T)^T}{(1+r_t)^t} right) ^{1/(T-t)}-1$



In your example: Spot rates are given by the zero coupon bonds meaning $r_1=0.02$, $r_2=0.03$. So you can compute the forward from year $t=1$ to $T=2$ by plugging in the above equation and the result is:$f_{1,2}=0.040098$






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    1 Answer
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    active

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

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    active

    oldest

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    3












    $begingroup$

    Let ${r_t}_{t>0}$ be the spotrates and $f_{t,T}$ be the forward rate from time $t$ to $T$ for $t<T$. Then the general formula to compute $f_{t,T}$ is
    $$
    (1+r_T)^T=(1+r_t)^t(1+f_{t,T})^{T-t}
    $$



    Now you can solve for $f_{t,T}$ to obtain:



    $f_{t,T}= left( frac{(1+r_T)^T}{(1+r_t)^t} right) ^{1/(T-t)}-1$



    In your example: Spot rates are given by the zero coupon bonds meaning $r_1=0.02$, $r_2=0.03$. So you can compute the forward from year $t=1$ to $T=2$ by plugging in the above equation and the result is:$f_{1,2}=0.040098$






    share|improve this answer











    $endgroup$


















      3












      $begingroup$

      Let ${r_t}_{t>0}$ be the spotrates and $f_{t,T}$ be the forward rate from time $t$ to $T$ for $t<T$. Then the general formula to compute $f_{t,T}$ is
      $$
      (1+r_T)^T=(1+r_t)^t(1+f_{t,T})^{T-t}
      $$



      Now you can solve for $f_{t,T}$ to obtain:



      $f_{t,T}= left( frac{(1+r_T)^T}{(1+r_t)^t} right) ^{1/(T-t)}-1$



      In your example: Spot rates are given by the zero coupon bonds meaning $r_1=0.02$, $r_2=0.03$. So you can compute the forward from year $t=1$ to $T=2$ by plugging in the above equation and the result is:$f_{1,2}=0.040098$






      share|improve this answer











      $endgroup$
















        3












        3








        3





        $begingroup$

        Let ${r_t}_{t>0}$ be the spotrates and $f_{t,T}$ be the forward rate from time $t$ to $T$ for $t<T$. Then the general formula to compute $f_{t,T}$ is
        $$
        (1+r_T)^T=(1+r_t)^t(1+f_{t,T})^{T-t}
        $$



        Now you can solve for $f_{t,T}$ to obtain:



        $f_{t,T}= left( frac{(1+r_T)^T}{(1+r_t)^t} right) ^{1/(T-t)}-1$



        In your example: Spot rates are given by the zero coupon bonds meaning $r_1=0.02$, $r_2=0.03$. So you can compute the forward from year $t=1$ to $T=2$ by plugging in the above equation and the result is:$f_{1,2}=0.040098$






        share|improve this answer











        $endgroup$



        Let ${r_t}_{t>0}$ be the spotrates and $f_{t,T}$ be the forward rate from time $t$ to $T$ for $t<T$. Then the general formula to compute $f_{t,T}$ is
        $$
        (1+r_T)^T=(1+r_t)^t(1+f_{t,T})^{T-t}
        $$



        Now you can solve for $f_{t,T}$ to obtain:



        $f_{t,T}= left( frac{(1+r_T)^T}{(1+r_t)^t} right) ^{1/(T-t)}-1$



        In your example: Spot rates are given by the zero coupon bonds meaning $r_1=0.02$, $r_2=0.03$. So you can compute the forward from year $t=1$ to $T=2$ by plugging in the above equation and the result is:$f_{1,2}=0.040098$







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 5 hours ago

























        answered 5 hours ago









        SanjaySanjay

        514314




        514314






















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