Geometric Brownian motion
$begingroup$
This question is related to conditional expectation of a geometric Brownian motion.
The price of a stock is $10$ times a Geometric Brownian Motion with drift $mu = 0.05$ and $sigma = 0.2$.
Assume the stock price is $30$ at time $16$. What is the expected value of the stock price at time $25$?
The answer is $56.3283$
What formula should I use to get this answer?
According to the question, the stock price is $S(t) = 10{e^{x(t)}}$
Should I use $E[Z(t)] = {e^{mu t + {{sigma {t^2}} over 2}}}$?
Thanks in advance.
probability
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
asked May 23 '13 at 12:48
rexrex
212
$endgroup$
add a comment |
$begingroup$
This question is related to conditional expectation of a geometric Brownian motion.
The price of a stock is $10$ times a Geometric Brownian Motion with drift $mu = 0.05$ and $sigma = 0.2$.
Assume the stock price is $30$ at time $16$. What is the expected value of the stock price at time $25$?
The answer is $56.3283$
What formula should I use to get this answer?
According to the question, the stock price is $S(t) = 10{e^{x(t)}}$
Should I use $E[Z(t)] = {e^{mu t + {{sigma {t^2}} over 2}}}$?
Thanks in advance.
probability
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
asked May 23 '13 at 12:48
rexrex
212
$endgroup$
$begingroup$
If you plug the numbers into your suggested equation for the expected value, does it match?
$endgroup$
– Trurl
May 23 '13 at 14:47
$begingroup$
Can you cite the question? I'm looking for a text that discusses such topics. (I realize this post is three years old and I'm talking to a ghost.)
$endgroup$
– Andrew
Feb 2 '16 at 20:33
add a comment |
$begingroup$
This question is related to conditional expectation of a geometric Brownian motion.
The price of a stock is $10$ times a Geometric Brownian Motion with drift $mu = 0.05$ and $sigma = 0.2$.
Assume the stock price is $30$ at time $16$. What is the expected value of the stock price at time $25$?
The answer is $56.3283$
What formula should I use to get this answer?
According to the question, the stock price is $S(t) = 10{e^{x(t)}}$
Should I use $E[Z(t)] = {e^{mu t + {{sigma {t^2}} over 2}}}$?
Thanks in advance.
probability
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
asked May 23 '13 at 12:48
rexrex
212
$endgroup$
This question is related to conditional expectation of a geometric Brownian motion.
The price of a stock is $10$ times a Geometric Brownian Motion with drift $mu = 0.05$ and $sigma = 0.2$.
Assume the stock price is $30$ at time $16$. What is the expected value of the stock price at time $25$?
The answer is $56.3283$
What formula should I use to get this answer?
According to the question, the stock price is $S(t) = 10{e^{x(t)}}$
Should I use $E[Z(t)] = {e^{mu t + {{sigma {t^2}} over 2}}}$?
Thanks in advance.
probability
probability
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
asked May 23 '13 at 12:48
rexrex
212
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
asked May 23 '13 at 12:48
rexrex
212
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
edited May 23 '13 at 13:53
Angela Richardson
5,25911733
5,25911733
asked May 23 '13 at 12:48
rexrex
212
asked May 23 '13 at 12:48
rexrex
212
asked May 23 '13 at 12:48
rexrex
212
212
$begingroup$
If you plug the numbers into your suggested equation for the expected value, does it match?
$endgroup$
– Trurl
May 23 '13 at 14:47
$begingroup$
Can you cite the question? I'm looking for a text that discusses such topics. (I realize this post is three years old and I'm talking to a ghost.)
$endgroup$
– Andrew
Feb 2 '16 at 20:33
add a comment |
$begingroup$
If you plug the numbers into your suggested equation for the expected value, does it match?
$endgroup$
– Trurl
May 23 '13 at 14:47
$begingroup$
Can you cite the question? I'm looking for a text that discusses such topics. (I realize this post is three years old and I'm talking to a ghost.)
$endgroup$
– Andrew
Feb 2 '16 at 20:33
$begingroup$
If you plug the numbers into your suggested equation for the expected value, does it match?
$endgroup$
– Trurl
May 23 '13 at 14:47
$begingroup$
If you plug the numbers into your suggested equation for the expected value, does it match?
$endgroup$
– Trurl
May 23 '13 at 14:47
$begingroup$
Can you cite the question? I'm looking for a text that discusses such topics. (I realize this post is three years old and I'm talking to a ghost.)
$endgroup$
– Andrew
Feb 2 '16 at 20:33
$begingroup$
Can you cite the question? I'm looking for a text that discusses such topics. (I realize this post is three years old and I'm talking to a ghost.)
$endgroup$
– Andrew
Feb 2 '16 at 20:33
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Under a geometric Brownian motion $$ dS_t = mu S_t {dt} + sigma S_t {dW_t} $$
where $mu = 0.05$ and $sigma = 0.2$,
the stock price is written $$ P_t = cS_t $$ where $c=10$.
Since $ mathbb{E}[S_t] = S_0 exp( mu t ) $, the expected stock value is
$$ mathbb{E}[P_t] = P_0 exp( mu t ) = 30 exp(0.05 t) $$
where we have shifted $t$ to "start" at $16$.
So at time $25$, we have $t=9$, so:
$$ mathbb{E}[P_t] = 30 exp(0.05 times 9) = 47.05 $$
which is wrong, apparently.
Either the question or I have made a mistake? Perhaps you can figure out which one?
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
$endgroup$
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: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
});
}
});
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%2fmath.stackexchange.com%2fquestions%2f400182%2fgeometric-brownian-motion%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
$begingroup$
Under a geometric Brownian motion $$ dS_t = mu S_t {dt} + sigma S_t {dW_t} $$
where $mu = 0.05$ and $sigma = 0.2$,
the stock price is written $$ P_t = cS_t $$ where $c=10$.
Since $ mathbb{E}[S_t] = S_0 exp( mu t ) $, the expected stock value is
$$ mathbb{E}[P_t] = P_0 exp( mu t ) = 30 exp(0.05 t) $$
where we have shifted $t$ to "start" at $16$.
So at time $25$, we have $t=9$, so:
$$ mathbb{E}[P_t] = 30 exp(0.05 times 9) = 47.05 $$
which is wrong, apparently.
Either the question or I have made a mistake? Perhaps you can figure out which one?
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
$endgroup$
add a comment |
$begingroup$
Under a geometric Brownian motion $$ dS_t = mu S_t {dt} + sigma S_t {dW_t} $$
where $mu = 0.05$ and $sigma = 0.2$,
the stock price is written $$ P_t = cS_t $$ where $c=10$.
Since $ mathbb{E}[S_t] = S_0 exp( mu t ) $, the expected stock value is
$$ mathbb{E}[P_t] = P_0 exp( mu t ) = 30 exp(0.05 t) $$
where we have shifted $t$ to "start" at $16$.
So at time $25$, we have $t=9$, so:
$$ mathbb{E}[P_t] = 30 exp(0.05 times 9) = 47.05 $$
which is wrong, apparently.
Either the question or I have made a mistake? Perhaps you can figure out which one?
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
$endgroup$
add a comment |
$begingroup$
Under a geometric Brownian motion $$ dS_t = mu S_t {dt} + sigma S_t {dW_t} $$
where $mu = 0.05$ and $sigma = 0.2$,
the stock price is written $$ P_t = cS_t $$ where $c=10$.
Since $ mathbb{E}[S_t] = S_0 exp( mu t ) $, the expected stock value is
$$ mathbb{E}[P_t] = P_0 exp( mu t ) = 30 exp(0.05 t) $$
where we have shifted $t$ to "start" at $16$.
So at time $25$, we have $t=9$, so:
$$ mathbb{E}[P_t] = 30 exp(0.05 times 9) = 47.05 $$
which is wrong, apparently.
Either the question or I have made a mistake? Perhaps you can figure out which one?
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
$endgroup$
Under a geometric Brownian motion $$ dS_t = mu S_t {dt} + sigma S_t {dW_t} $$
where $mu = 0.05$ and $sigma = 0.2$,
the stock price is written $$ P_t = cS_t $$ where $c=10$.
Since $ mathbb{E}[S_t] = S_0 exp( mu t ) $, the expected stock value is
$$ mathbb{E}[P_t] = P_0 exp( mu t ) = 30 exp(0.05 t) $$
where we have shifted $t$ to "start" at $16$.
So at time $25$, we have $t=9$, so:
$$ mathbb{E}[P_t] = 30 exp(0.05 times 9) = 47.05 $$
which is wrong, apparently.
Either the question or I have made a mistake? Perhaps you can figure out which one?
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
answered Jan 13 at 20:10
user3658307user3658307
4,5933946
4,5933946
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics 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%2fmath.stackexchange.com%2fquestions%2f400182%2fgeometric-brownian-motion%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
$begingroup$
If you plug the numbers into your suggested equation for the expected value, does it match?
$endgroup$
– Trurl
May 23 '13 at 14:47
$begingroup$
Can you cite the question? I'm looking for a text that discusses such topics. (I realize this post is three years old and I'm talking to a ghost.)
$endgroup$
– Andrew
Feb 2 '16 at 20:33