How to calculate one-year forward one-year rate?
$begingroup$
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
asked 7 hours ago
Marie kMarie k
91
New contributor
Marie k is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
add a comment |
$begingroup$
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
asked 7 hours ago
Marie kMarie k
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.
$endgroup$
4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
7 hours ago
add a comment |
$begingroup$
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
asked 7 hours ago
Marie kMarie k
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.
$endgroup$
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
asked 7 hours ago
Marie kMarie k
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.
asked 7 hours ago
Marie kMarie k
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.
asked 7 hours ago
Marie kMarie k
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.
asked 7 hours ago
Marie kMarie k
91
asked 7 hours ago
Marie kMarie k
91
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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:$f_{1,2}=0.040098$
answered 5 hours ago
SanjaySanjay
514314
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add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
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votes
$begingroup$
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:$f_{1,2}=0.040098$
answered 5 hours ago
SanjaySanjay
514314
$endgroup$
add a comment |
$begingroup$
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:$f_{1,2}=0.040098$
answered 5 hours ago
SanjaySanjay
514314
$endgroup$
add a comment |
$begingroup$
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:$f_{1,2}=0.040098$
answered 5 hours ago
SanjaySanjay
514314
$endgroup$
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:$f_{1,2}=0.040098$
answered 5 hours ago
SanjaySanjay
514314
edited 5 hours ago
answered 5 hours ago
SanjaySanjay
514314
answered 5 hours ago
SanjaySanjay
514314
answered 5 hours ago
SanjaySanjay
514314
514314
add a comment |
add a comment |
Marie k is a new contributor. Be nice, and check out our Code of Conduct.
Marie k is a new contributor. Be nice, and check out our Code of Conduct.
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4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
7 hours ago