Mixing
Quadratic Covariation of an Increasing Process with another Process is 0
$begingroup$
According to the book I'm reading on Option Pricing:
Since $V$ is an increasing process, $langle X, V rangle_t = langle V rangle_t = 0$
In this case $X$ is just a price process (according to the book the specific form shouldn't matter, but the process is assumed to be a continuous local martingale)
Does anyone see why this is true? Are there specific conditions under which it is true, or is it just for any increasing process?
I found a similar unanswered question, but wanted to try again: Quadratic Variation of Increasing Process?
Thanks a lot!
stochastic-processes stochastic-calculus martingales
asked Jan 29 at 23:30
SladeSlade
59111
$endgroup$
add a comment |
$begingroup$
According to the book I'm reading on Option Pricing:
Since $V$ is an increasing process, $langle X, V rangle_t = langle V rangle_t = 0$
In this case $X$ is just a price process (according to the book the specific form shouldn't matter, but the process is assumed to be a continuous local martingale)
Does anyone see why this is true? Are there specific conditions under which it is true, or is it just for any increasing process?
I found a similar unanswered question, but wanted to try again: Quadratic Variation of Increasing Process?
Thanks a lot!
stochastic-processes stochastic-calculus martingales
asked Jan 29 at 23:30
SladeSlade
59111
$endgroup$
$begingroup$
The quadratic covariation of an increasing process with a continuous process is zero. That's a general statement which is not very difficult to show using the very definition of the quadratic covariation.
$endgroup$
– saz
Jan 30 at 7:23
$begingroup$
Cross-posted: quant.stackexchange.com/questions/43789/…
$endgroup$
– LocalVolatility
Jan 30 at 7:43
add a comment |
$begingroup$
According to the book I'm reading on Option Pricing:
Since $V$ is an increasing process, $langle X, V rangle_t = langle V rangle_t = 0$
In this case $X$ is just a price process (according to the book the specific form shouldn't matter, but the process is assumed to be a continuous local martingale)
Does anyone see why this is true? Are there specific conditions under which it is true, or is it just for any increasing process?
I found a similar unanswered question, but wanted to try again: Quadratic Variation of Increasing Process?
Thanks a lot!
stochastic-processes stochastic-calculus martingales
asked Jan 29 at 23:30
SladeSlade
59111
$endgroup$
According to the book I'm reading on Option Pricing:
Since $V$ is an increasing process, $langle X, V rangle_t = langle V rangle_t = 0$
In this case $X$ is just a price process (according to the book the specific form shouldn't matter, but the process is assumed to be a continuous local martingale)
Does anyone see why this is true? Are there specific conditions under which it is true, or is it just for any increasing process?
I found a similar unanswered question, but wanted to try again: Quadratic Variation of Increasing Process?
Thanks a lot!
stochastic-processes stochastic-calculus martingales
stochastic-processes stochastic-calculus martingales
asked Jan 29 at 23:30
SladeSlade
59111
asked Jan 29 at 23:30
SladeSlade
59111
asked Jan 29 at 23:30
SladeSlade
59111
asked Jan 29 at 23:30
SladeSlade
59111
asked Jan 29 at 23:30
SladeSlade
59111
59111
$begingroup$
The quadratic covariation of an increasing process with a continuous process is zero. That's a general statement which is not very difficult to show using the very definition of the quadratic covariation.
$endgroup$
– saz
Jan 30 at 7:23
$begingroup$
Cross-posted: quant.stackexchange.com/questions/43789/…
$endgroup$
– LocalVolatility
Jan 30 at 7:43
add a comment |
$begingroup$
The quadratic covariation of an increasing process with a continuous process is zero. That's a general statement which is not very difficult to show using the very definition of the quadratic covariation.
$endgroup$
– saz
Jan 30 at 7:23
$begingroup$
Cross-posted: quant.stackexchange.com/questions/43789/…
$endgroup$
– LocalVolatility
Jan 30 at 7:43
$begingroup$
The quadratic covariation of an increasing process with a continuous process is zero. That's a general statement which is not very difficult to show using the very definition of the quadratic covariation.
$endgroup$
– saz
Jan 30 at 7:23
$begingroup$
The quadratic covariation of an increasing process with a continuous process is zero. That's a general statement which is not very difficult to show using the very definition of the quadratic covariation.
$endgroup$
– saz
Jan 30 at 7:23
$begingroup$
Cross-posted: quant.stackexchange.com/questions/43789/…
$endgroup$
– LocalVolatility
Jan 30 at 7:43
$begingroup$
Cross-posted: quant.stackexchange.com/questions/43789/…
$endgroup$
– LocalVolatility
Jan 30 at 7:43
add a comment |
0
active
oldest
votes
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%2f3092878%2fquadratic-covariation-of-an-increasing-process-with-another-process-is-0%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3092878%2fquadratic-covariation-of-an-increasing-process-with-another-process-is-0%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
$begingroup$
The quadratic covariation of an increasing process with a continuous process is zero. That's a general statement which is not very difficult to show using the very definition of the quadratic covariation.
$endgroup$
– saz
Jan 30 at 7:23
$begingroup$
Cross-posted: quant.stackexchange.com/questions/43789/…
$endgroup$
– LocalVolatility
Jan 30 at 7:43