Calculation of an European option
$begingroup$
Say a process $X$ satisfies for $s>t$ $$X_t=mathbb{E}[(K-(yH_s)^{alpha})^+|H_t]$$
for some positive constants $y$ and $K$ and $alphain mathbb{R}$. The process $H$ is given by $$H_t=expBig(frac{1}{2}theta^2t+theta W_tBig)$$
for some positive $theta$ and $W$ is a Wiener process, so $X$ is the price of a European put option on $yH_t$ where $y$ is a scaling of sorts. I am looking for a way to isolate $y$ on the left hand side and $X$ on the other, like $$y=f(X_t)$$
for a suitable function $f$ in which $y$ does $textit{not}$ appear. I tried formulating the expectation as an integral but it doesn't really get me anywhere. Have I missed a trick?
finance
asked Dec 9 '18 at 22:25
j.doej.doe
83
$endgroup$
add a comment |
$begingroup$
Say a process $X$ satisfies for $s>t$ $$X_t=mathbb{E}[(K-(yH_s)^{alpha})^+|H_t]$$
for some positive constants $y$ and $K$ and $alphain mathbb{R}$. The process $H$ is given by $$H_t=expBig(frac{1}{2}theta^2t+theta W_tBig)$$
for some positive $theta$ and $W$ is a Wiener process, so $X$ is the price of a European put option on $yH_t$ where $y$ is a scaling of sorts. I am looking for a way to isolate $y$ on the left hand side and $X$ on the other, like $$y=f(X_t)$$
for a suitable function $f$ in which $y$ does $textit{not}$ appear. I tried formulating the expectation as an integral but it doesn't really get me anywhere. Have I missed a trick?
finance
asked Dec 9 '18 at 22:25
j.doej.doe
83
$endgroup$
add a comment |
$begingroup$
Say a process $X$ satisfies for $s>t$ $$X_t=mathbb{E}[(K-(yH_s)^{alpha})^+|H_t]$$
for some positive constants $y$ and $K$ and $alphain mathbb{R}$. The process $H$ is given by $$H_t=expBig(frac{1}{2}theta^2t+theta W_tBig)$$
for some positive $theta$ and $W$ is a Wiener process, so $X$ is the price of a European put option on $yH_t$ where $y$ is a scaling of sorts. I am looking for a way to isolate $y$ on the left hand side and $X$ on the other, like $$y=f(X_t)$$
for a suitable function $f$ in which $y$ does $textit{not}$ appear. I tried formulating the expectation as an integral but it doesn't really get me anywhere. Have I missed a trick?
finance
asked Dec 9 '18 at 22:25
j.doej.doe
83
$endgroup$
Say a process $X$ satisfies for $s>t$ $$X_t=mathbb{E}[(K-(yH_s)^{alpha})^+|H_t]$$
for some positive constants $y$ and $K$ and $alphain mathbb{R}$. The process $H$ is given by $$H_t=expBig(frac{1}{2}theta^2t+theta W_tBig)$$
for some positive $theta$ and $W$ is a Wiener process, so $X$ is the price of a European put option on $yH_t$ where $y$ is a scaling of sorts. I am looking for a way to isolate $y$ on the left hand side and $X$ on the other, like $$y=f(X_t)$$
for a suitable function $f$ in which $y$ does $textit{not}$ appear. I tried formulating the expectation as an integral but it doesn't really get me anywhere. Have I missed a trick?
finance
finance
asked Dec 9 '18 at 22:25
j.doej.doe
83
asked Dec 9 '18 at 22:25
j.doej.doe
83
asked Dec 9 '18 at 22:25
j.doej.doe
83
asked Dec 9 '18 at 22:25
j.doej.doe
83
asked Dec 9 '18 at 22:25
j.doej.doe
83
83
add a comment |
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%2f3033123%2fcalculation-of-an-european-option%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%2f3033123%2fcalculation-of-an-european-option%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
