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
New contributor
$endgroup$
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
New contributor
$endgroup$
4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
4 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
New contributor
$endgroup$
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
New contributor
New contributor
New contributor
asked 4 hours ago
Marie kMarie k
91
91
New contributor
New contributor
4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
4 hours ago
add a comment |
4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
4 hours ago
4
4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
4 hours ago
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
4 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:$f_{1,2}=0.040098$
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "204"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Marie k is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f44081%2fhow-to-calculate-one-year-forward-one-year-rate%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
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:$f_{1,2}=0.040098$
$endgroup$
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:$f_{1,2}=0.040098$
$endgroup$
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:$f_{1,2}=0.040098$
$endgroup$
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:$f_{1,2}=0.040098$
edited 2 hours ago
answered 3 hours ago
SanjaySanjay
515314
515314
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.
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.
Thanks for contributing an answer to Quantitative Finance Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f44081%2fhow-to-calculate-one-year-forward-one-year-rate%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
4
$begingroup$
(1+0.02)*(1+x) = (1+0.03)^2 Solve for x.
$endgroup$
– Alex C
4 hours ago